Post on 17-Feb-2023
INFORMATION TO USERS
This material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted.
The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction.
1 .T he sign or "target" for pages apparently lacking from the document photographed is "Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity.
2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image. You will find a good image of the page in the adjacent frame.
3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photcing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete.
4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from "photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific pages you wish reproduced.
5. PLEASE NOTE: Some pages may have indistinct print. Filmed as received.
Xerox University Microfilms300 North Z eeb RoadAnn Arbor, Michigan 48106
73-23,943
JAYROE, J r . , R obert Rhea, 1940-UNSUPERVISED SPATIAL CLUSTERING WITH SPECTRAL DISCRIMINATION.
The U n iv e rs ity o f Oklahoma, P h .D ., 1973 P h y s ic s , g e n e ra l
University Microfilms, A XEROX Company, Ann Arbor, Michigan
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.
THE UNIVERSITY OF OKLAHOMA
GRADUATE COLLEGE
UNSUPERVISED SPATIAL CLUSTERING WITH SPECTRAL DISCRIMINATION
A DISSERTATION
SUBMITTED TO THE GRADUATE FACULTY
in p a r t i a l f u l f i l lm e n t o f th e requ irem en ts fo r th e
degree of
DOCTOR OF PHILOSOPHY
BY
ROBERT R. JAYROE, JR.
N om an, Oklahoma
1972
UNSUPERVISED SPATIAL CLUSTERING WITH SPECTRAL DISCRIMINATION
APPROVED BY
iT i f n '
DISSERTATION COMMITTEE
ACKNOWLEDGMENT
This work i s subm itted to th e G raduate College of th e U n iv e rs ity of
Oklahoma in p a r t i a l f u l f i l lm e n t o f th e requirem ents fo r th e degree of
D octor o f P h ilosophy .
The au th o r w ishes to ex p ress h is s in c e re s t g ra t i tu d e and ap p rec ia
t io n to h is Major P ro fe s so r , Dr. R. G. Fow ler, of th e Department of
P hysics and Astronomy a t th e U n iv e rs ity of Oklahoma fo r p rov id ing
a s s is ta n c e , m orale and guidance th roughout th e e n t i r e graduate
cu rricu lum ..
The au th o r a lso w ishes to ex p ress a s in c e re ap p re c ia tio n to
Dr. F. R. K rause o f th e N a tio n a l A eronau tics and Space A dm in istra tio n ,
George C. M arshall Space F l ig h t C en te r, Aero-Astrodynamics L aborato ry ,
H u n ts v il le , Alabama, and th e T ra in in g Branch o f M arshall Space F lig h t
C enter fo r p rov id in g th e o p p o rtu n ity of co n tin u in g ed u ca tion , working
ex p erien ce and perform ing in te r e s t in g re s e a rc h .
In a d d i t io n , th e au th o r w ishes to exp ress h is g ra ti tu d e to
Mr. M elvin R. P h i l l ip s o f th e ITT R esearch I n s t i t u t e , who performed
th e program ing fo r in te r f a c in g th e c l a s s i f i c a t i o n programs w ith th e
v a r io u s in p u t-o u tp u t d ev ices and fo r in te g ra t in g th e se programs in to the
E arth R esources P ro cesso r Computer Program developed under h is c o n tra c t ,
NAS8-26797.
iii
The au th o r w ishes to acknowledge D r. H arry W. Smedes o f th e
U nited S ta te s G eo lo g ica l Survey , D enver, C o lorado , f o r h is many
in t e r e s t in g d is c u s s io n s and co o p e ra tio n and f o r sup p ly in g th e raw
d a ta , ground t r u t h , and e v a lu a tio n o f r e s u l t s f o r th e Y ellow stone
P ark t e s t s i t e .
The au th o r a ls o w ishes to acknowledge Dr. David Landgrebe and
Mr. T erry P h i l l ip s o f Purdue U n iv e rs i ty f o r su p p ly in g th e d a ta and
ground t r u t h fo r th e Purdue F l ig h t L ine Cl t e s t s i t e .
T his work was perform ed a t th e George C. M arsh a ll Space F l ig h t
C en te r, H u n ts v i l le , Alabama, and i s in su p p o rt o f th e Alabama E a rth
R esources Technology S a t e l l i t e 1 in v e s t ig a t io n and M arsh a ll Space
F l ig h t C e n te r’s Skylab E arth R esources E xperim en ta l Package
I n v e s t ig a t io n 560M.
IV
TABLE OE CONTENTS
Page
LIST OF TABLES.......................................................................................................................... v i
LIST OF F IG U R E S ................................................................................................................... v i i
C hapter
I . INTRODUCTION .................................................................................................. 1
I I . SYNOPSIS ON FEATURE EXTRACTION .......................................................... 3
I I I . UNSUPERVISED FEATURE EXTRACTION............................................................13
IV. RESULTS .............................................................................................................28
V. CONCLUSIONS........................................................................................................ 72
LIST OF REFERENCES................................................................................................................. 76
APPENDIX A PROGRAM DESCRIPTION..................................................................................78
APPENDIX B COMPUTER PROGRAM L IS T IN G S .....................................................................82
APPENDIX C CHANNEL DEPENDENCE CONSIDERATIONS ............................................. 104
V
LIST OF TABLES
Table Page
1. Channel and W avelength Correspondence ................................................... 29
2. Ground T ru th In fo rm atio n .................................................................................. 32
3. M erging P rocedu re fo r F i r s t 40 C l u s t e r s ..................................................34
4. Merging P rocedure fo r C lu s te rs 4 1 - 7 9 ................................................... 35
5. Merging P rocedure fo r C lu s te rs 2 5 - 5 2 ................................................... 37
6. M u ltip le C lu s te r F ie ld s ................................................................................. 38
7. F e a tu re Symbol and D e s c r ip t i o n ........................................................................40
8. User I n te r p r e ta t i o n o f R e s u l t s ....................................................................... 41
9. Merging P rocedu re fo r Y ellow stone D a t a ......................................................57
10. I n te r p r e ta t i o n o f Y ellow stone R e c r u i t s ......................................................58
V i
LIST OF FIGURES
Figure Page
1. Data C o lle c tio n P la tfo rm Showing Sensor O utputs and
A ssocia ted F ea tu re V ecto rs . . . . . . . . . . . .................. 6
2 . Program Logic F lo w ........................................................................................14
3. F lig h t Line Cl - A e r ia l Pho to , C lu s te r S e le c tio n and
I n i t i a l C la s s i f ic a t io n ................................................................................ 31
4 . F in a l Cl C la s s i f ic a t io n Map - S ec tio n 1 ............................................ 42
5. F in a l Cl C la s s i f ic a t io n Map - S ec tio n 2 ............................................ 43
6. F in a l Cl C la s s i f i c a t io n Map - S ec tio n 3 ............................................ 44
7. F in a l Cl C la s s i f ic a t io n Map - S ec tio n 4 ............................................ 45
8. F in a l Cl C la s s i f ic a t io n Map - S ec tio n 5 ............................................ 46
9. F in a l Cl C la s s i f ic a t io n Map - S ec tio n 6 ............................................ 47
10. F in a l Cl C la s s i f i c a t io n Map - S ec tio n 7 ..................................... . 48
11. F in a l Cl C la s s i f i c a t io n Map - S ec tio n 8 ............................................ 49
12. F in a l Cl C la s s i f ic a t io n Map - S ec tio n 9 .............................................50
13. F in a l Cl C la s s i f i c a t io n Map - S ec tion 1 0 .............................................51
14. F in a l Cl C la s s i f i c a t io n Map - S ec tio n 1 1 .............................................52
15. F in a l Cl C la s s i f i c a t io n Map - S ec tion 12 . . ............................... 53
16. Y ellow stone P ark - Video R e p rin t, C lu s te r S e le c tio n ,
I n i t i a l C la s s i f ic a t io n and Secondary C lu s te r S e le c tio n . . . 55
17. F in a l Y ellow stone Park C la s s i f ic a t io n Map - S ec tio n 1 . . . . 60
vii
LIST OF FIGURES (co n tin u ed )
F ig u re Page
18. F in a l Y ellow stone P ark C la s s i f i c a t io n Map - S ec tio n 2 . • . .61
19. F in a l Y ellow stone P ark C la s s i f i c a t io n Map - S ec tio n 3 . • . .62
20. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 4 . • . .63
21. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 5 . • . .64
22. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 6 . • . .65
23. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 7 . • . . 66
24. F in a l Y ellow stone P ark C la s s i f i c a t io n Map — S ec tio n 8 . • . .67
25. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 9 . ■ . .68
26. F in a l Y ellow stone P ark C la s s i f i c a t io n Map - S ec tio n 10. • . .69
27. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 11. • . .70
28. F in a l Y ellow stone Park C la s s i f i c a t io n Map - S ec tio n 12. • . .71
29. Channels 1 and 2 Mean V alues . . . . . 106
30.
31. Channels 1 and 2 V ariances ................... o 110
32. Channel 1 V ariances and C ovariances w ith Channel 2 • • ' . I l l
33.
34. Channel 1 V ariances and C ovariances w ith Channel 3 . . . . 113
V l l l
UNSUPERVISED SPATIAL CLUSTERING WITH SPECTRAL DISCRIMINATION
CHAPTER I
INTRODUCTION
The o b je c tiv e o f t h i s r e s e a rc h i s th e co n v ers io n o f rem o te ly sensed
d a ta in to u s e fu l in fo rm a tio n re g a rd in g th e lo c a t io n and d i s t r i b u t i o n o f
v a r io u s c la s s e s o f i d e n t i f i a b l e .ea rth o b s e rv a tio n f e a tu r e s . The rem o te ly
sensed d a ta i s c o l le c te d from a p la tfo rm , which may be an a i r p la n e , a
s h ip , a b a llo o n o r a s a t e l l i t e . The se n so rs used g e n e ra lly c o l l e c t
e le c tro m a g n e tic r a d ia t io n in s p e c if ie d w avelength i n t e r v a l s (m u lt i-
s p e c t r a l and therm al s c a n n e rs , o th e r ty p e s o f ra d io m e te rs , and m u ltiband
p h o to g rap h y ), echo r e tu rn s ( s id e lo o k in g a e r i a l ra d a r and so n ar) and
m agnetic f i e l d in fo rm a tio n (m agnetom eter), to name a few. The c o l le c te d
d a ta may be an a lo g , d i g i t a l o r a ph o to g rap h ic im age; and th e d a ta i s
fo rm a tted such th a t a one to one correspondence i s p re se rv e d betw een
th e ground scene and th e d a ta , a s in an a e r i a l ph o to g rap h . The d a ta
i s th en analyzed to d e te rm in e what f e a tu r e s can be e x tra c te d from th e
d a ta and to determ ine th e lo c a t io n and th e d i s t r i b u t i o n o f th e se
f e a tu r e s . Examples of f e a tu r e s could be crop ty p e s , d is e a se d c ro p s ,
bo d ies o f w a te r , w a te r p o l lu t io n and lan d ty p e s . M u ltitu d e s o f o th e r
ty p es o f f e a tu r e s e x i s t . As p r e s e n t ly u se d , th e r e a re th r e e m ain ty p es
o f f e a tu r e e x t r a c t io n m ethods, w hich w i l l be deno ted by human photo
1
2
i n t e r p r e t a t i o n , su p e rv ise d com puter f e a tu r e e x t r a c t io n , and u n superv ised
com puter f e a tu r e e x t r a c t io n . The f i r s t two f e a tu r e e x t r a c t io n methods
in v o lv e human su p e rv is io n and judgm ent a f t e r th e f a c t , w hereas th e
t h i r d method does n o t pe rm it any change o f c r i t e r io n from datum to
datum . The u n su p erv ised com puter f e a tu r e e x t r a c t io n method i s based
e n t i r e ly on a lo g ic a l s e t o f m a th em atica l r u le s designed to e x t r a c t th e
f e a tu r e s p re s e n te d in th e rem o te ly sensed d a ta . T his r e p o r t d is c u s s e s
th e th re e m ost commonly used ty p e s o f f e a tu r e e x t ra c t io n methods and
p re s e n ts a r e c e n t ly developed com puter program fo r u n superv ised f e a tu r e
e x t r a c t io n .
CHAPTER II
SYNOPSIS ON FEATURE EXTRACTION
The most u n iv e rs a l method of f e a tu r e e x tra c tio n i s th e c l a s s i c a l
a r t of photo in t e r p r e ta t io n . This a r t i s p r im a rily a p rocess of v is u a l
in s p e c t io n and s u b je c t iv e a n a ly s is by a tra in e d human o b se rv e r, and i t
h as been g r e a t ly enhanced by a v a r ie ty o f in s trum en ts and machines
( s te r e o v ie w e rs , m ic ro d en s ito m e te rs , a u to p lo t te r s , f a ls e co lo r image
enhancem ent, e t c . ) . The hum an's r o le in t h i s ta s k i s to su b je c tiv e ly
combine v is u a l ly a c q u ire d in p u ts r e l a t i n g to s p a t i a l p ro p e r t ie s , c o lo r ,
te x tu r e and tem poral phenomena to id e n t i f y and c la s s i fy o b je c ts in th e
1 2 3ground scen e . ’ ’ In perform ing th i s ta sk th e human ex e rc ise s a
s o p h is t ic a te d a b i l i t y to combine v a r io u s types of d a ta and draw
co n c lu sio n s as to in fo rm a tio n s u b t l e t i e s p re s e n t. As an example of t h i s
s o p h is t ic a t io n , co n s id e r th e land u se c l a s s i f i c a t i o n s , "p as tu re" and
"improved p a s tu r e ." Improved p a s tu re i s p a s tu re th a t i s surrounded by a
fe n c e , b u t from an a e r i a l pho tograph , fen ces a re o f te n d i f f i c u l t to
o b serv e . Grazing an im als , however, develop th e h a b it of walking along
th e fen ce s and th e photo in t e r p r e te r m erely has to look fo r a brown path
su rround ing a green f i e l d . The most obvious and se r io u s inadequacy of
photo i n t e r p r e ta t io n i s th e amount o f manpower and tim e needed to
an a ly ze la r g e volumes o f d a ta r e s u l t in g from rem ote sensing oh a la rg e
a re a s c a le .
3
4
Because o f t h i s inadequacy, more and more em phasis i s be ing p laced
on develop ing computer techn iq u es fo r an a ly z in g la rg e volumes o f
rem o te ly sensed d a ta . P re sen t computer tech n iq u es a re designed to
e x p lo it th e s p e c t r a l in fo rm atio n of imagery o r o f s p e c t r a l scanners f o r
e x tra c t in g in fo rm a tio n . One approach to t h i s te ch n iq u e i s to use a d a ta
bank. The u se o f a d a ta bank assumes th a t an o b je c t o r an a re a of
s u f f i c i e n t dim ensions in th e ground scene to be considered homogeneous
p o sse sse s a unique s p e c t r a l s ig n a tu re . The s p e c tr a l s ig n a tu re s a re
produced by re c o rd in g th e re tu rn e d energy (combined r e f le c te d and
r a d ia te d e lec tro m ag n e tic energy) in each o f a number o f narrow and
d is c r e t e w avelength in t e r v a l s . The d a ta bank would co n ta in p re s to re d o r
e m p ir ic a lly d e riv e d s t a t i s t i c s on th e s ig n a tu re s o f known o b je c ts o r i t
would c o n ta in th e a b i l i t y to model and a n a ly t ic a l ly c a lc u la te what a
g iven s ig n a tu re should be.
The d i f f i c u l t y w ith t h i s techn ique i s th a t th e re i s a p p re c ia b le
v a r i a b i l i t y in th e s ig n a tu r e s , which i s due to n a tu ra l tem poral changes
as w e ll as man-made changes. In p r a c t ic e , t h i s v a r i a b i l i t y i s ev id en t
even fo r re p e a te d o b se rv a tio n s in which g re a t c a re i s taken to m a in ta in
c o n s ta n t sun a n g le , view ing a n g le , cloud co v er, am bient tem p era tu re and
h um id ity , in s tru m en t c a l ib r a t io n , e tc . T his v a r i a b i l i t y can be
a t t r ib u t e d to a la rg e degree to a la c k o f m icro sco p ic homogeneity
between g ro s s ly id e n t ic a l o b je c ts o r sp e c ie s in two d i f f e r e n t ground
scen es . For exam ple, no two le av es of d ise a se d corn w i l l appear e x a c tly
th e same, and no two rows of corn w i l l be a rray ed e x a c tly th e same o r be
surrounded by th e same c o lo r o f ground exposed between th e s t a lk s . Thus,4
th e problem o f s ig n a tu re com parison le a d s to modeling th e o ry .
D
A nother s e r io u s drawback to t h i s te ch n iq u e i s th e amount o f computer
memory re q u ire d to s to r e a l l p o s s ib le s ig n a tu re s and t h e i r v a r i a t io n s ,
and a p r o h ib i t iv e amount o f computer tim e re q u ire d to compare an
unknown s p e c t r a l s ig n a tu re w ith a l l p o s s ib le s ig n a tu re s s to re d in th e
d a ta bank, u n le ss a ta b le look up p rocedu re can be u se d .^
The n ex t approach to be d e sc r ib e d i s p robab ly th e most p o p u la r and
w idely used com puter f e a tu r e e x t r a c t io n te c h n iq u e . This approach has
been developed e x te n s iv e ly a t Purdue U n iv e rs i ty ,^ and many r e la te d
te c h n iq u e s '^ and improvements have been d e riv e d from t h i s approach .
This te ch n iq u e w i l l be c a l le d th e su p erv ised c l a s s i f i c a t i o n tech n iq u e
s in c e i t r e q u ir e s human su p e rv is io n f o r th e s e le c t io n o f t r a in in g a re a s ,
which u l t im a te ly de te rm in e th e number and types o f f e a tu r e s to be
e x t r a c te d , as w e ll as th e accuracy o f c l a s s i f i c a t i o n .
In o rd e r to d e s c r ib e t h i s te c h n iq u e , i t w i l l be n e c e ssa ry f i r s t to
d e s c r ib e th e d a ta c o l le c t io n and fo rm a ttin g , as w e ll as to develop th e
m athem atical n o ta t io n fo r o p e ra tin g on th e d a ta . A m u l t i s p e c t r a l scanner
i s g e n e ra lly used fo r th e d a ta c o l le c t io n . The scan n er i s a monochromator
w ith a d e te c to r a r ra y fo r re c o rd in g th e r e f le c te d and e m itted r a d ia t io n
from th e ground in d i f f e r e n t w avelength in t e r v a l s . The monochromator i s
mounted in an a i r c r a f t and th e r o ta t in g m irro r scans th e ground scene as
th e a i rp la n e f l i e s , p roducing an analog s ig n a l as shown in F ig u re 1. I f
th e d e te c to r a r ra y c o n ta in s n d e te c to r s , th en n s im u ltaneous s ig n a ls o r
channe ls o f d a ta a re reco rd ed f o r th e same ground scen e . The analog
d a ta i s th en d ig i t i z e d and reco rded on m agnetic ta p e to produce an n -
d im ensional d i g i t a l image of th e ground scen e . Let th e a lg e b ra ic v a lu e
of th e d i g i t a l number d e riv e d from th e analog s ig n a l be denoted by j^x^^
TRACES ON MULTICHANNEL O SC ILLO SC O P E
X : D e te c to r Center WovelengthX : X ,
Channel n Ampl i tude
i * -
h iX = Xi
Channel 2 Amplitude
Channel i Ampl i tude
X : X o
y = y on-D IM E N S IO N A L F E A T U R E VECTOR TAKEN FROM SIGNAL TRACE FOR A RESOLUTION ELEM ENT A T ( x ^ , /<, }
Amplitude 11 kError Bars Indicate Uncertainty in Feature Vector Signoture Due to Instrument Variabi l i ty, l l luroinotion, Polar iza t ion, Atmospheric E f fec ts , etc.
CUTAMAY VIEW OF A IR C R A F T SHOWING INSTRUMENTATION
Monochromator and D e tec to r Array
Tope RecorderOscilloscope
iEntrance Slit
RotatingMirror
I/ I Stat ionaryI I Mirrorf I
Iy, Ground Scene
Coordinate and. Scanning Direction
Ground Scene With Three Different Ref lectance and Emittonce Regions
Resolution Element Field of View at ( x * , y^)
-• X •* / **■ -V / ^ X •** ** **
X , Ground Scene Coordinate and Fl ight Direction
FIG. 1. DATA C O L L E C T I O N P L A T F O R M SHOWING SENSOR O U T P U T S A N D A S S O C I A T E D F E A T U R E V E C T O R S
7
w here k = l th e channel number o r w avelength in te r v a l ;
1=1, 2 , 3 ......... .. A, th e scan l i n e number o r x c o o rd in a te o f th e ground
scen e ; and j = l , 2 , . . . . , m, th e sam ple number fo r scan i o r th e y
c o o rd in a te o f th e ground scen e .
Thus, th e d a ta s e t c o l le c te d co n ta in s n channels o f d a ta , S, scan
l i n e s , and m d i g i t a l sam ples p e r scan p e r channel w ith an am plitude
g iv en by . Each ground scene c o o rd in a te , i and j , o f th e d ig i t a l
image i s no rm ally c a l le d a r e s o lu t io n elem ent and each r e s o lu t io n
elem ent i s th e re f o r e d e sc rib e d by an n -d im ensional v e c to r c a l le d a
f e a tu r e v e c to r , The components o f th e f e a tu re v e c to r a re =
t i * i j ' 2 * i j ' '" 'n % i j ] '
The nex t s te p i s to produce a boundary map^^ so th a t i t may be
compared w ith an a e r i a l pho tograph tak en of th e ground scene a t the
same tim e th a t th e m u l t i s p e c t r a l scanner d a ta was c o l le c te d . The
boundary map and a e r i a l pho tograph a re shown in Chapter 4 and a method
fo r p roducing a boundary map w i l l be d iscu ssed in th e nex t s e c tio n . The
photograph a llo w s an o b se rv e r to s e l e c t , f o r example, a rea s which appear
to be crops and th en to lo c a te th e scan l i n e and column number of th e
d a ta co rresp o n d in g to th o se crops from th e boundary map. The d a ta may15
th en be accessed fo r a n a ly s is and used as a t r a in in g a re a .
For i d e n t i f i c a t i o n o f crop s p e c ie s , ground t r u t h in fo rm atio n i s
r e q u ir e d , u n le s s a d a ta bank i s a v a i la b le . The ground t r u th in fo rm a tio n
cou ld be c o l le c te d by an o b se rv e r v i s i t i n g each f i e l d o r o b ta in in g th e
in fo rm a tio n from a fa rm er as to th e crop ty p e . I t i s in t e r e s t in g to n o te
th a t t h i s ty p e o f in fo rm a tio n c o l le c t io n has o c c a s io n a lly been erroneous
and p re s e n t c l a s s i f i c a t i o n te ch n iq u es have been s u f f i c i e n t ly a c c u ra te
8
to p o in t o u t th e se e r r o r s . With t h i s in fo rm a tio n , th e f i e l d s in th e
a e r i a l photograph can be la b e le d acco rd in g to crop ty p e . • T ra in in g
a re a s a r e th en s e le c te d from th e boundary map co rrespond ing to
p a r t i c u l a r known f i e l d s in th e a e r i a l pho tograph . The d e s ire d
s t a t i s t i c s a re c a lc u la te d from th e d a ta in th e t r a in in g a re a and a
s t a t i s t i c a l d e c is io n r u le i s used fo r c l a s s i f y in g th e rem ain ing d a ta
in th e d i g i t a l image. A com puter map o f th e ground scene i s th e n
p r in te d o u t showing th e lo c a t io n o f a l l r e s o lu t io n elem ents th a t w ere
c l a s s i f i e d acco rd ing to th e s t a t i s t i c a l d e c is io n r u le as be long ing o r
b e in g s im ila r to th e p a r t i c u l a r t r a in in g a re a s s e le c te d . The computer
map can be compared w ith th e ground t r u t h in fo rm a tio n in th e a e r i a l
photograph f o r accu racy . A ccu rac ies o f 80 to 90 p e rc e n t a re n o t ;
uncommon.
One o f th e most w idely used d e c is io n r u le s i s th e maximum
lik e l ih o o d r a t i o te c h n iq u e . The developm ent o f t h i s te ch n iq u e depends
upon two ty p e s o f d e c is io n e r r o r s th a t can be made in th e c l a s s i f i c a t i o n .
The f i r s t ty p e of e r r o r i s n o t a s s ig n in g a f e a tu r e v e c to r as b e long ing
to a c la s s when i t a c tu a l ly d o es . The second ty p e o f e r ro r i s a s s ig n in g
a f e a tu r e v e c to r to a c la s s when in a c t u a l i t y i t does n o t belong .
W eights a re u s u a lly a ss ig n ed to b o th ty p e s o f e r r o r s depending on how
c o s t ly th e e r r o r i s in making th e wrong d e c is io n . These w e ig h ts ,
a r e r e f e r r e d to as c o s t f a c to r s and a r e a s s o c ia te d w ith c l a s s i fy in g a
f e a tu r e v e c to r , x , b e lo n g in g to c la s s i in to c la s s j .
U ltim a te ly , th e d e c is io n p ro ced u re m ust be a b le to in d ic a te a f i n a l
cho ice f o r each p o in t in th e n -d im en sio n a l f e a tu r e sp ace . The f e a tu r e
sp a c e , R, must be d iv id e d in to m m u tu a lly e x c lu s iv e re g io n s , R^, R g , . . .^ ^ .
9L et th e p r o b a b i l i ty d e n s ity fu n c tio n fo r sam ples from c la s s i be
f^ (x ) and th e a p r i o r i p ro b a b il i ty of occu rrence o f c la s s i be P^. The
p r o b a b i l i ty o f m is c la s s ify in g a sample from c la s s i in to c la s s j i s
P ( j | i ) = f f (x )dx , (1)
" j
and th e c o n d itio n a l expected c o s t i f th e sample i s from c la s s i i s
m mC. = E L . . P ( j | i ) = E L . . / f . ( x ) d x . (2)
j= l j= l
One u s e fu l c r i t e r io n th a t i s o f te n used i s th e average co s t which i s
g iven by
m m mC = E P.C. = E f E L . . P . f . ( x ) d x , (3)
i = l ^ ^ j = l Rj i = l ^ ^
and th e reg io n s R^ R^ a re chosen to m inim ize th e average c o s t . Them
average co s t i s minimized i f th e in teg ran d E L . .P . f . ( x ' ' i s a minimum,i= l ^ ^
which i s e q u iv a le n t to d ec id in g th a t a sample x i s from c la s s j i f
m mE L . . P . f . ( x ) £ E L P . f . ( x ) fo r a l l k={=j (4)i= l ^ ^ i= l 1 1m
By s u b tra c t in g E L . . P . f . ( x ) from bo th s id e s , th e d e c is io n r u le i s i= l ^ ^
o b ta in e d , x i s in c la s s j i f
. ,3,£,(x) (Lj, -
Since th e c o s t f a c to r s L^^ and th e a p r i o r i p r o b a b i l i t i e s P^ a re
c o n s ta n ts , th e d e c is io n r u le th a t m inim izes th e average r i s k i s th e
r a t i o o f two c o n d itio n a l p ro b a b il i ty d e n s i t ie s o r l ik e lih o o d r a t i o s w ith
a th re sh o ld v a lu e . The c o s t f a c to r s and a p r i o r i p r o b a b i l i t i e s a re used
10
only in de term in ing th e th re s h o ld v a lu e . W ith a sim ple ch o ice o f c o s t
. f a c t o r s , = 0 f o r c o r r e c t c l a s s i f i c a t i o n , = 1 w ith i^ j fo r
m is c la s s i f ic a t io n and eq u a l a p r i o r i p r o b a b i l i t i e s , th e d e c is io n r u le
reduces to d ec id in g th a t x i s in c la s s j i f
f j ( x ) > f^Xx) f o r a l l k=fj ‘ (6)
T his i s g e n e ra lly r e f e r r e d to as th e maximum lik e l ih o o d d e c is io n r u le .
In a c tu a l p r a c t ic e th e c o s t f a c t o r s , a p r i o r i p r o b a b i l i t i e s , and
th e p r o b a b i l i ty d i s t r i b u t io n s a re n o t known, b u t must be e s tim a te d from
members o f each t r a in in g a re a . The v a r io u s c l a s s i f i c a t i o n tech n iq u es
th a t have been developed a re e s s e n t i a l l y d i f f e r e n t methods f o r e s tim a tin g
th e p r o b a b i l i ty d i s t r i b u t io n s .
In most cases a m u l t iv a r ia te G aussian d i s t r i b u t io n i s assumed fo r
th e t r a in in g a re a d a ta ; and th e v e c to r means, M^, and co v arian ce m a tr ic e s ,
V^, a re c a lc u la te d from th e d a ta in each t r a in in g a re a . Because th e
G aussian d i s t r i b u t io n i s e x p o n e n tia l , th e lo g a rith m o f th e d e c is io n r u le
i s u sed . Thus, d ec id e th a t x belongs to c la s s j fo r a l l k^ j i f
l og^ | V. | + ( x - S . ) V ‘ ^(x-M .) < log^lVj^l + ( x - M ^ ) \ '^ ( î - M j^ ) , (7)
where |v^[ and ^ a re th e d e te rm in an t and in v e rse o f th e co v arian ce
m a trix and T deno tes th e tra n s p o se o p e ra tio n o f a m a tr ix .
The advantage o f th e su p e rv ised tech n iq u e i s th a t w ith a v a i la b le
ground t r u t h , known a re a s o f p a r t i c u l a r i n t e r e s t can be used to lo c a te
s im ila r a re a s elsew here in th e d a ta . The d isad v an tag e o f th e su p erv ised
te ch n iq u e i s th e manual s e le c t io n o f t r a in in g a re a s from th e d a ta , w hich,
when a p p lie d to la rg e d a ta volum es, can become as te d io u s and as tim e
consuming as th e a r t o f photo i n t e r p r e t a t i o n . T his i s e s p e c ia l ly t r u e of
h ig h a l t i t u d e m u l t is p e c tr a l a e r i a l photography.
11
In re c e n t y e a r s , th e amount of rem o te ly sensed d a ta c o l le c te d on
e a r th o b se rv a tio n s has been phenom enal, as ev idenced by p u b lic a t io n s in
th e l i t e r a t u r e . T h e f u tu r e o u tlo o k in d ic a te s th a t t h i s d a ta
c o l le c t io n w i l l co n tin u e to grow, as shown by E arth R esources Technology
S a t e l l i t e s 1 and 2 , th e Skylab E a rth R esources Experim ent Package and
th e Space S h u tt le S o r t ie L ab o ra to ry . Because th e volume of d a ta
expected appears to be g e t t in g ou t o f hand , much em phasis i s being
p laced on th e developm ent o f un su p erv ised tech n iq u es f o r f e a tu r e
e x t r a c t io n . These computer tech n iq u es a re designed to e x t r a c t f e a tu r e s
from rem otely sensed d a ta w ith o u t e i th e r th e a s s is ta n c e and su p e rv is io n
o f an o b se rv e r o r th e p r io r b e n e f i t of ground t r u t h in fo rm a tio n .
R eferences 18 and 19 g iv e a re c e n t rev iew of th e s t a t e - o f - t h e - a r t of
th e se te c h n iq u e s . The p re s e n t d isad v an tag es o f th e unsuperv ised
tech n iq u es a re th a t a h ig h degree of c l a s s i f i c a t i o n accuracy i s o f te n
d i f f i c u l t to o b ta in and che computer tim e i s r e l a t i v e ly e x te n s iv e .
Thus, th e s p e c i f i c problem to a t ta c k i s th e developm ent o f an
unsuperv ised f e a tu r e e x t r a c t io n program th a t c l a s s i f i e s w ith a h igh
degree of accu racy . The com puter tim e re q u ire d can th en be more
e f f i c i e n t l y u t i l i z e d by o p tim iz in g th e com puter program lo g ic ,
program ing in an e f f i c i e n t machine language, and by u sing s p e c ia l
purpose com puters. The advantage of th e u n su p erv ised te ch n iq u e i s th a t
no p r io r ground t r u t h in fo rm a tio n i s re q u ire d b e fo re th e d a ta a n a ly s is .
The r e s u l t s o b ta in ed w ith th e u n su p erv ised tech n iq u e a re designed to
show th e lo c a t io n and d i s t r i b u t io n of th e e x tra c te d f e a tu r e s , b u t no
id e n t i f i c a t i o n of th e f e a tu r e s i s p o s s ib le w ith o u t ground t r u t h
in fo rm a tio n . Thus, th e r e s u l t s o f th e u n su p erv ised tech n iq u e can be
12
used f o r d i r e c t in g ground t r u t h p a t r o l s and th e lo c a t io n and amount of
ground t r u t h needed can be a c c u ra te ly determ ined b e fo re any ground
t r u t h i s c o l le c te d . The adequa te d e te rm in a tio n o f where and how much
ground t r u t h to c o l l e c t i s an im p o rtan t economic c o n s id e ra tio n when d a ta
i s c o l le c te d on a g lo b a l o r even a re g io n a l b a s i s . I f d a ta i s c o l le c te d
on a s e a so n a l i n t e r v a l , f o r exam ple, f u tu r e ground t r u t h c o l le c t io n can
be m inim ized by m o n ito rin g th e f e a tu r e s ig n a tu re s as a fu n c tio n of
seaso n . I f some o f th e s e s ig n a tu re s change s ig n i f i c a n t ly from p a s t
= ra-3u lts , th e c l a s s i f i c a t i o n map can be used to d i r e c t ground t r u t h
p a t r o l s to update on ly th o se f e a tu r e i d e n t i f i c a t i o n s which have changed.
In o rd e r to m a in ta in c u r re n t in fo rm a tio n on c u r re n t accom plishm ents
in rem ote s e n s in g , th e "P roceed ings o f th e I n te r n a t io n a l Symposia on
Remote Sensing of th e E nvironm ent," p u b lish e d by th e W illow Run
L a b o ra to r ie s , U n iv e rs ity o f M ichigan , and th e "Annual E a rth R esources
A i r c r a f t Program S ta tu s Review ," p u b lish e d by NASA, a re h ig h ly
recommended along w ith th e l i t e r a t u r e survey l i s t e d in R eference 17.
The n e x t C hapter d is c u s s e s a proposed u n superv ised computer
program fo r f e a tu r e e x t r a c t io n .
CHAPTER I I I
UNSUPERVISED FEATURE EXTRACTION
F ea tu re e x t r a c t io n from rem ote ly sensed d a ta i s a v e ry complex
p ro c e s s . For t h i s re a so n , no com prehensive model o r e x p l i c i t e x te rn a l
c r i t e r i a e x i s t fo r d e f in in g and e x t r a c t in g a l l f e a tu r e s . The s e le c t io n
o f t r a in in g a re a s f o r f e a tu r e e x t r a c t io n in tro d u c e s th e b ia s o f human
o b se rv a tio n and p reconceived judgm ent in to th e c l a s s i f i c a t i o n c r i t e r i a .
For exam ple, an o b serv er may s e le c t a t r a in in g a re a c o n ta in in g corn in
o rd e r to a ttem p t to c l a s s i f y corn in a l l o th e r p o r tio n s o f th e ground
scen e , w h ile th e d a ta from th a t t r a in in g a re a may on ly be cap ab le of
c la s s i fy in g a l l s p a rs e ly grow ing, sm all g reen p la n ts surrounded by b a re
s o i l .
The ph ilosophy behind th e developm ent o f t h i s c l a s s i f i c a t i o n
program i s to accep t t e n ta t i v e ly an in t e r n a l c r i t e r i o n ; th a t i s , th e
d a ta i t s e l f should n a tu r a l ly su g g es t th e f e a tu r e s to be e x tra c te d and
su b seq u en tly id e n t i f i e d .
A flow c h a r t of su c c e s s iv e s ta g e s o f th e computer program i s shown
in F ig u re 2.
The f i r s t s ta g e o f th e program i s to produce a boundary map o f th e
d a ta by s e p a ra tin g th e d a ta in to homogeneous and inhomogeneous a re a s .
T his i s accom plished by com puting th e average f e a tu r e v e c to r s p e c t r a l
13
14
ISTAGE ONE
INPUT RAW DATA
CALCULATESTATISTICS
OUTPUTBOUNDARYTAPE
Î
RAW DATA TAPE
STA G E TWO
INPUTBOUNDARYTAPE
USE PXP ARRAYTO LOCATE 2
INITIAL CLUSTERS
OUTPUT TAPECONTAINING MAPOF BOUNDARYAND CLUSTERLOCATIONS
STAG E TH R EE
INPUT TAPES CONTAINING LOCATIONS OF CLUSTERS AND RAW DATA
CALCULATE STATISTICS AND DO SPECTRAL MERGING
SAVE STATISTICS OF FINAL CLASSES
S T A G E FOUR
INPUT BOUNDARY AND RAW DATA TAPES AND STATISTICS FOR CLASSIF ICATION
CLASSIFY DATA AND UPDATE BOUNDARY TAPE TO CONTAIN BOUNDARIES AND CLASSES
OUTPUT BOUNDARY AND CLASSIFICATION TAPE
DECREASE PXP ARRAY TO QXQ AND INPUT BOUNDARY AND CLASSIFICATION TAPE
ISCLASSIFICATION OF GROUND SCENE
COMPLETE?
I- - - - - - - -YES
OUTPUT FINAL RESULTS
FIG. 2. P R O G R A M L O G I C F L O W
15
d is ta n c e p e r channel o r d im ension in th e d i r e c t io n o f the x and y
ground scene c o o rd in a te s . The fo rm ulas fo r th i s c a lc u la tio n a re
g iven by
n 1 / r-, n/ 2 and s =y
(8)
where i and j a re th e scan l i n e and scan l i n e column number, r e s p e c t iv e ly ,
o f th e d a ta in th e d i g i t a l image and th e summation i s over n channels o f
d a ta .
These s p e c t r a l d is ta n c e s a re c a lc u la te d fo r each r e s o lu t io n elem ent
and s to re d in a j o i n t p r o b a b i l i ty d i s t r i b u t io n , P (s^ , s ^ ) . The average
f e a tu r e v e c to r d is ta n c e p e r dim ension i s computed to determ ine a m easure
o f change p re s e n t in th e d a ta from one r e s o lu t io n element to th e nex t
and a lso to keep th e numbers o ccu rrin g in th e c a lc u la t io n in th e same
ra n g e , r e g a rd le s s o f th e number o f dim ensions used. The a rea s o f th e
d a ta where th e s p e c t r a l change, in e i th e r th e x o r y ground scene
c o o rd in a te d i r e c t io n , i s equal to o r le s s th an th e average s p e c t r a l
change w i l l be c l a s s i f i e d as a homogeneous re s o lu t io n elem ent; o th e rw ise ,
th e r e s o lu t io n elem ent w i l l be c l a s s i f i e d as a boundary. The average
d is ta n c e s o f th e average f e a tu r e v e c to r s p e c tr a l d is ta n c e p e r channel a re
computed u s in g th e form ulas
4 ' 4 '“=x'“=y’
Sy - 1 ! Sy P(s^^Sy) d s /S y , and (10)
Vy ■ ":%Sy P(Sx.Sy) ds ds . (ID
16
These c a lc u la t io n s a re used f o r d e f in in g a d e c is io n boundary in th e
j o i n t p r o b a b i l i ty d i s t r i b u t io n as to what com bination of x and y
s p e c t r a l d is ta n c e s a re c l a s s i f i e d as belo n g in g to a homogeneous
r e s o lu t io n elem ent o r a boundary r e s o lu t io n e lem en t. The d e c is io n
boundary i s in th e shape of an e l l i p s e which may have p r in c ip a l axes
in d i r e c t io n s o th e r th an s and s , The d i r e c t io n and m agnitude o fX y
20th e p r in c ip a l axes a re c a lc u la te d from th e e ig e n v e c to rs and
e ig en v a lu es a s s o c ia te d w ith th e m a tr ix
X ®x®y
I Vy
(12)
The eq u a tio n of th e e l l i p s e in th e p r in c ip a l axes c o o rd in a te system
I S
. ' 2
= 1, (13)
w here s ' and- s ' a re th e d is ta n c e s s and s r o ta te d in to th e p r in c ip a l X y X y
axes c o o rd in a te system by th e e ig en v ec to r tra n s fo rm a tio n , s ' ^ andX y
a re th e e ig en v a lu es o r h a l f le n g th s o f th e p r in c ip a l axes squared .
. ' 2
(14)
i s th en ro ta te d back in to th e s , s c o o rd in a te system by th e in v e rs ex ’ y
17
e ig e n v e c to r tra n s fo rm a tio n to o b ta in th e eq u a tio n o f th e e l l i p s e on th e
d e c is io n boundary in th e s ^ , c o o rd in a te system . The e q u a tio n o f th e
e l l i p s e i s g iven by
as^ + bs^ + cs s = 1 , (15)X y X y
where a , b , c a re de term ined from r o ta t in g (1 4 ). The d e c is io n i s to
c l a s s i f y a r e s o lu t io n elem ent as b e ing homogeneous i f
as^ + bs^ + cs s < 1 . (16)X y X y —
A d i g i t a l image o f a boundary map i s reco rd ed on m agnetic ta p e fo r use
in th e second s ta g e o f p ro c e s s in g . The m agnetic ta p e map u t i l i z e s -1
to d e s c r ib e a boundary elem ent and zero fo r a homogeneous e lem en t.
The second s ta g e i s concerned w ith th e s e le c t io n and s p a t i a l
m erging o f unknown c a n d id a te f e a tu r e s based upon th e hom ogeneity o f th e
ground sc e n e , as d isp la y e d by th e boundary map reco rd ed on th e m agnetic
ta p e . Because th e b o u n d arie s on th e map a re n o t c lo sed and have open
gaps in some c a s e s , th e problem i s to s e le c t homogeneous a re a s w ith a
m a th em atica l lo g ic th a t w i l l p rev en t th e s e a re a s from c o n ta in in g a
m ix tu re o f d i f f e r e n t f e a tu r e s . This i s accom plished by u s in g a f ix e d
shape p X p r e s o lu t io n elem ent a r ra y which moves th rough th e boundary
map on ly in th e x o r y ground scene c o o rd in a te d i r e c t io n . I n i t i a l l y , a
homogeneous a re a in th e boundary map i s found which i s la rg e enough fo r
th e a r r a y to f i t i n to . The a re a covered by th e a r ra y i s d e s ig n a te d as
belo n g in g to c l u s t e r 1. The a r ra y i s allow ed to move in t h i s a re a u n t i l
a boundary i s encoun tered and th en th e d i r e c t io n of movement must be
changed. A ll r e s o lu t io n elem ents f a l l i n g w ith in th e movement o f th e
f ix e d a r r a y a re s a id to belong to c l u s t e r 1 , and th e ze ro s p re v io u s ly
o c c u rr in g on th e boundary map in th e s e lo c a t io n s a re changed to +1. A fte r
18
th e a r ra y can no lo n g e r move and en g u lf new r e s o lu t io n e lem en ts , an o th e r
lo c a t io n i s found w hich w i l l c o n ta in th e p x p a r ra y . A ll r e s o lu t io n
élém ents f i t t i n g in to t h i s a r ra y w i l l be d e s ig n a te d as be long ing to
c lu s t e r 2 . The p ro cess i s re p e a te d u n t i l a l l o f th e boundary map d a ta
has been exh au sted . C lu s te rs which p h y s ic a l ly touch on th e boundary map
a re merged and c a l le d th e same c l u s t e r . This i s c a l le d s p a t i a l m erging,
which w i l l be c o n tra s te d w ith s p e c t r a l m erging l a t e r . A fte r s p a t i a l
m erging , th e c lu s t e r s a re renumbered so th a t th e c lu s t e r numbers w i l l
have a con tinuous range from 1 ...........,N. The o u tp u t of t h i s second s ta g e
i s an o th e r map co n ta in in g th e numbers - 1 , 0 , 1 , 2 , . . . . , N, w ith -1
in d ic a t in g boundary r e s o lu t io n e lem en ts , 0 in d ic a t in g homogeneous
r e s o lu t io n elem ents n o t encountered by th e moving f ix e d shape a r r a y , and
1 , 2 , . . . . , N in d ic a t in g r e s o lu t io n elem ents be long ing to c lu s t e r s 1 , 2 ,
. . . . , N, r e s p e c t iv e ly . The f ix e d shape a r r a y , i f chosen la rg e enough,
w i l l n o t p erm it th e m ixing o f f e a tu r e s because th e open gaps in th e
b o u n d arie s w i l l be so sm all compared to th e a r ra y s iz e th a t th e a r ra y
w i l l n o t be a b le to p ass th rough th e boundary. On m u l t is p e c tr a l scanner
d a ta taken a t an a l t i t u d e o f 2600 f e e t , a 10 x 10 a r ra y i s s u f f i c i e n t to
keep d i f f e r e n t f e a tu r e s s e p a ra te . T h is a ls o p ro v id es a minimum sample
s iz e o f 100, which i s a very adequa te sam ple on which to base s t a t i s t i c a l
c a lc u la t io n s . T y p ic a lly , most m u l t is p e c tr a l d a ta i s c o l le c te d a t h ig h e r
a l t i t u d e s so th a t a 10 x 10 a r ra y w i l l , in g e n e ra l , be s u f f i c i e n t to
p rev en t th e m ixing of f e a tu r e s . The m agnetic ta p e c o n ta in in g th e
bo u n d arie s and lo c a t io n s o f c lu s t e r s and th e m agnetic ta p e c o n ta in in g th e
raw d a ta a r e th e in p u ts to th e th i r d s ta g e o f p ro c e s s in g .
19
The t h i r d s ta g e o f p ro cess in g i s concerned w ith s p e c t r a l m erging
o f th e s e le c te d unknown c an d id a te f e a tu r e s . The boundary and c lu s te r
map ta p e g iv es th e lo c a tio n s of th e raw d a ta on th e raw d a ta tap e
belong ing to each c l u s t e r . The mean f e a tu r e v e c to rs and co v ariance
m a tr ic e s , c , a re c a lc u la te d fo r each c lu s t e r u sing th e form ulas
1
km^jl " k ^ i£ m^U " ^k^£^ ^m^£^ ’
where x i s th e a lg e b ra ic v a lu e of th e i*"^ sample in th e k o r m^^ channel
of th e c lu s t e r c o n ta in in g sam ples. The mean v a lu e o f th e samples
in th e k^^ channel o f th e c lu s t e r i s g iven by ^x^, w h ile th e
co v arian ce between channels k and m of th e c lu s t e r i s g iven by
, c „ . These c a lc u la t io n s a re used to d e f in e d e c is io n boundaries w ith km Jo
which to p h y s ic a l ly surround th e d a ta belong ing to a c lu s te r in
n -d im en sio n a l sp ace . The most g e n e ra l c lo sed su rfa c e th a t can be used
to surround th e n -d im en sio n a l d a ta i s an n -d im ensional h y p e re l l ip s e .
The c e n tro id of th e c lu s te r e l l i p s e i s g iven by th e f e a tu r e v e c to r mean
v a lu e s w h ile th e p r in c ip a l axes d i r e c t io n and m agnitude can be
determ ined by th e e ig e n v e c to r tra n s fo rm a tio n as was d iscu ssed when
E quations (12) th ro u g h (14) were in tro d u ced .
In a s t a t i s t i c a l sen se , th e e ig en v ec to r tra n s fo rm a tio n on th e
co v arian ce m a trix lo c a te s th e d i r e c t io n o f o rth o g o n a l p r in c ip a l axes fo r
21which th e v a r ia n c e s a re minimized and maximized . The v a r ia n c e s a re
th e d ia g o n a l elem ents o f th e covarian ce m a trix and th e o f f d iag o n a l
20
e lem en ts, c o v a ria n c e s , a re made zero by th e tra n s fo rm a tio n . Thus, th e
eq u a tio n o f an n -d im en sio n a l e l l i p s e in reduced form i s o b ta in ed fo r
each c l u s t e r , and, in g e n e ra l, each c lu s t e r w i l l have a d i f f e r e n t
co o rd in a te system . The n ex t s te p i s to d e r iv e a d e c is io n r u le fo r
de term in ing how many c lu s t e r s a c tu a l ly re p re s e n t th e same f e a tu r e .
This d e c is io n i s now based e n t i r e ly upon s p e c t r a l in fo rm a tio n r a th e r
th an th e s p a t i a l in fo rm a tio n which was used in E quations (12) th rough
(1 4 ). The d e c is io n r u le i s th a t two c lu s te r s re p re s e n t th e same f e a tu r e
i f th e c e n tro id s o f b o th c lu s t e r s a re co n ta in ed in b o th c l u s t e r s ’
e l l i p s e s . A lthough th i s s p e c t r a l merging p ro ced u re was d e riv e d from
22p h y s ic a l i n t u i t i o n , a theorem was lo c a te d w hich adds m athem atical
p re c is io n . The theorem s t a t e s th a t th e o rth o g o n a l tra n s fo rm a tio n
which m inim izes th e mean square d is ta n c e between a s e t o f v e c to rs from
th e c l u s t e r , s u b je c t to th e c o n s tr a in t th a t th e volume of th e space
i s in v a r ia n t under tra n s fo rm a tio n , i s a r o t a t i o n , E^, fo llow ed by a
d iag o n a l tra n s fo rm a tio n , The rows of th e m a tr ix E^ a re th e e ig en
v e c to rs of th e co v arian ce m a tr ix , c^ , of th e s e t o f v e c to r s , and th e
elem ents o f a re th o se g iven in E quation (1 9 ), where ^^c^ i s th e
s tan d a rd d e v ia tio n o f th e c o e f f i c ie n t s o f th e s e t o f v e c to rs in th e
d i r e c t io n o f th e e ig e n v e c to r o f c^ .
The d iag o n a l e lem ents o f th e d iag o n a l tra n s fo rm a tio n , a re given
by
n 1
- 7 7 T • (W )j j &
21
The r a t i o n a le beh ind th i s theorem , as p re se n te d in R eference 2 3, m e r i ts
some d is c u s s io n as ap p lied to s p e c t r a l m erging. This d is c u s s io n w i l l
a lso apply to s p e c t r a l c l a s s i f i c a t i o n , which i s to be d esc rib e d l a t e r .
I t i s d e s i r a b le to have a m easure o f s im i l a r i t y between two c l u s t e r s ,
S“^ , f o r d e c id in g w hether o r n o t two c lu s t e r s a re to be merged. L et
V be th e mean fe a tu r e v e c to r o f one c l u s t e r , w ith components g iven
by e q u a tio n (1 7 ) , and l e t be th e e n t i r e s e t o f f e a tu r e v e c to rs con
ta in e d in th e o th e r c lu s t e r s w ith th e s u b s c r ip t on deno ting th e m*- v e c to r
o f th e s e t . The s im i la r i ty may be reg a rd ed as a mean square s p e c t r a l d i s
ta n c e and shou ld d e sc r ib e th e c lo se n e ss o f v to th e e n t i r e s e t o f f e a tu r e
v e c to r s , ( x ^ . A ccording to th e p h ilo sophy o f R eference 23 , th e d e f in i t i o n o f
" d is ta n c e " does no t n e c e s s a r i ly mean E uclidean d is ta n c e , bu t may mean .
" c lo se n e ss" in some a r b i t r a r y , a b s t r a c t p ro p e rty o f th e s e t {x^} which
has y e t to be determ ined . The use o f an undeterm ined d is ta n c e measure
does n o t a l t e r th e d e f in i t io n o f s im i l a r i t y , bu t p ro v id es an o rd e rin g
which s im i la r i ty la c k s . M ath em atica lly , th e s im i la r i ty S ^ (v ,{ x ^} ) of
a f e a tu r e v e c to r v and a s e t of f e a tu r e v e c to rs {x^} exem plify ing a
c l u s t e r can be w r i t t e n as
MS ^ (v , {x^}) = ^ Z d^(v , x^>, (20)
m=l
where th e d is ta n c e m easure, d^( ) , has n o t y e t been s p e c if ie d . The
in v e rse of S i s used because th e sm a lle r th e d is ta n c e , th e more s im i la r i ty .
One p o s s ib le way to choose th e d is ta n c e m easure i s to u t i l i z e th e
knowledge th a t th e s e t {x } d e sc r ib e s one f e a tu r e , and', th e r e f o r e , th em
members of th e s e t should a l l be very s im i la r o r c lo s e . F urtherm ore ,
th e members o f th e s e t could be made even more s im i la r by u s in g f e a tu r e
22
w eig h tin g c o e f f i c i e n t s , and m in im izing th e av erag e i n t e r c l u s t e r
d is ta n c e o f a l l th e members o f th e s e t . Thus, th e e q u a tio n to .b e
m inim ized i s
D? =Mg Mg nZ Z I = minimum.
p^= l mj^=l k= l ^(21)
thw here k r e p re s e n ts th e k component o f th e f e a tu r e v e c to r and m and p^
r e p re s e n t th e m^^ and p^^ f e a tu r e v e c to r o f th e s e t Ü c o n ta in in g
members.
In o rd e r to m inim ize E quation (2 1 ) , some c o n s t r a in t must be p la ced
on th e f e a tu r e w e ig h tin g c o e f f i c i e n t s . S e v e ra l a l t e r n a t iv e s a re
p o s s ib le , b u t th e m ost ap p ea lin g c o n s t r a in t i s
n(22)
I f th e f e a tu r e w eig h tin g c o e f f i c ie n t s a re co n s id e re d to be th e
d im ensions o f a hypercube , th e n E quation (22) i s a c o n s ta n t volume
c o n s t r a in t . In o rd e r to m inim ize E quation (21) needs to be w r i t t e n
in a more co n v en ien t form .
— Mj n
2m=l “ Jl ^bp2= l
2M, nz
----------------------2M, n,w ! ( .x g - .x . )= Z -2
th
(23)
w here i s th e v a r ia n c e o f th e k*"" d im ension o f th e f e a tu r e v e c to r s in
s e t a . Using th e c o n s t r a in t and an undeterm ined m u l t i p l i e r , th e
m inim izing e q u a tio n becomes
23
= 0 f o r j = l , 2 , ......... ..... (24)
which may be r e w r i t te n as
k k^ i/ T
k * l(25)
U sing th e c o n s tr a in t fo r de te rm in in g X g iv e s
kk^&
nn
p=i
V n
k°A(26)
The f e a tu r e w eig h tin g c o e f f i c ie n t s in d ic a te th a t i f th e v a r ia n c e in a
p a r t i c u l a r dim ension i s sm a ll, th en th e v a lu e o f th e f e a tu r e can be
a n t ic ip a te d w ith a h ig h degree o f accu racy and should be h e a v i ly w eighed.
On th e o th e r hand , i f th e v a r ia n c e i s l a r g e , th en l i t t l e w eigh t shou ld be
a t ta c h e d to th a t f e a tu r e .
E quation (26) i s th e d ia g o n a l tra n s fo rm a tio n d isc u sse d in th e
theorem encom passing E quation (19) and i s i d e n t i c a l to E quation (1 9 ). As
th e theorem s t a t e s , t h i s d is ta n c e m easure can be a d d i t io n a l ly m inim ized
by app ly ing th e e ig e n v e c to r tr a n s fo rm a tio n . I t fo llo w s by E quations (18)
and (21) th a t th e s im i la r i ty c r i t e r i o n , E quation (2 0 ), fo r d ec id in g
w hether to merge two c lu s t e r s k and Ü i s g iven by
- p V “
n(27)
24
where v, i s th e mean f e a tu r e v e c to r o r c e n tro id fo r c lu s t e r k , and {x } k
a re th e f e a tu r e v e c to rs belong ing to c lu s te r &.
S u b s t i tu t in g E quation (19) fo r g ives
. V 2
PP
V n
p=i p p V(28)
The d e c is io n fo r m erging two c lu s t e r s w i l l now depend on th e th re sh o ld
v a lu e g iven to t ’ e a s r s of s im i la r i ty fo r bo th c l u s t e r s . A th re sh o ld
v a lu e can be d(^ c a lc u la t in g th e average s im i la r i ty w ith in a
c l u s t e r , which i s g iven by
% . l
n ^p^m. " p*&)E ------— ------—
p=l p p V+ n
n Vn2n. (29)
(30)
Using E quation (29) as a th re s h o ld v a lu e fo r E quation (28) g iv e s th e
d e c is io n r u l e , merge c lu s t e r s k and Si i f
p= i pp^&
N otice th a t E quation (30) i s th e eq u a tio n o f a h y p e re l l ip s e in th e
p r in c ip a l axes c o o rd in a te s , which was e a r l i e r d e riv ed by p h y s ic a l
i n t u i t i o n . N o tice a lso th a t th e th re s h o ld v a lu e n i s independent o f
c lu s t e r and depends on ly on th e dim ension of th e f e a tu r e sp ace . 'T hus,
i f an e l l i p t i c a l boundary d e c is io n ru le i s used in th e p r in c ip a l a x is
c o o rd in a te system , th e theorem can be extended to say th a t th e d iag o n a l
tra n s fo rm a tio n i s n o t needed and on ly th e e ig en v ec to r tra n s fo rm a tio n i s
25
needed s in c e th e th re sh o ld can always be w r i t t e n as some c o n s ta n t tim es
A fte r th e i n i t i a l M s e t o f c lu s t e r s has been merged in to a f i n a l N
s e t o f c l u s t e r s , w ith N ^ M, th e e ig e n v e c to r r o ta t io n m a trix and th e
eq u a tio n fo r th e h y p e re l l ip s e in p r in c ip a l axes c o o rd in a te s a re s to re d
in memory fo r each f i n a l c l u s t e r . The c lu s t e r s a re now c a l le d c la s s e s
s in c e each c la s s re p re s e n ts a s t a t i s t i c a l l y d i f f e r e n t f e a tu r e p re se n te d
by th e d a ta . The re g io n s in f e a tu r e space R^, R^ co rrespond ing
to each c la s s a re d i s t i n c t s in c e no more m erging i s p o s s ib le . This
f e a tu r e e x t r a c t io n in fo rm a tio n i s now ready f o r use in th e l a s t s ta g e of
p ro c e ss in g .
The f i n a l s ta g e o f p ro c e ss in g i s concerned w ith c la s s i fy in g th e
d a ta in th e d i g i t a l image o f th e ground scene and showing th e lo c a t io n
and d i s t r i b u t io n o f th e f e a tu r e s . The in p u ts to t h i s s ta g e o f p ro c e ss in g
a re th e raw d a ta ta p e , th e s t a t i s t i c s f o r each c la s s and th e boundary
ta p e . The d e c is io n r u le f o r .c l a s s i f y in g a r e s o lu t io n elem ent f e a tu r e
v e c to r V in to c la s s i i s g iven by
p=i PP a
which i s th e same as E quation (30) excep t f o r th e f a c to r o f two. The
f a c to r o f two i s j u s t i f i e d based on th e fo llo w in g argum ents. F i r s t , th e
d e c is io n r u le f o r c la s s i fy in g a r e s o lu t io n elem ent can be more le n ie n t
than th e d e c is io n r u le f o r m erging two c l u s t e r s . The e r r o r s of
m ism erging a re more pronounced in th e c l a s s i f i c a t i o n th a n th e
m is c la s s i f ic a t io n o f in d iv id u a l r e s o lu t io n e lem en ts. Secondly , th e
26
e x p re ss io n on th e l e f t hand s id e o f th e in e q u a l i ty in E quation (31) i s
id e n t ic a l to th e argument in th e ex p o n e n tia l o f a d i s j o i n t m u l t iv a r ia te
G aussian d i s t r i b u t io n . Thus, a r e s o lu t io n elem ent i s n o t c l a s s i f i e d as
belo n g in g to a c la s s i f th e n -d im en sio n a l e x p o n e n tia l n - f o ld s . F u r th e r
j u s t i f i c a t i o n fo r u s in g E quations (30) and (31) and th e th re sh o ld
v a lu e s o f n and 2n r e s p e c t iv e ly i s th a t th e term s co n ta in ed in th e
summation a re c h i-sq u a re d i s t r i b u te d , and a c h i-s q u a re d i s t r i b u t io n has
a m ean-value n and v a r ia n c e 2n, where n i s th e number o f d eg rees of
, 23freedom .
The d a ta o b ta in ed from th e raw d a ta ta p e i s c l a s s i f i e d acco rd ing
to th e d e c is io n r u le in E quation (31) and th e r e s u l t o f th e c l a s s i f i
c a t io n i s updated on th e boundary ta p e map. For exam ple, i f a r e s o lu t io n
elem ent belongs to c l a s s 3 , a 3 i s p la ced on th e boundary ta p e a t th e
lo c a t io n o f th e r e s o lu t io n e lem en t. I f a r e s o lu t io n elem ent i s no t
c l a s s i f i e d as be long ing to any c l a s s , no change i s made on che boundary
ta p e . I f a r e s o lu t io n elem ent can be c l a s s i f i e d as be lo n g in g to s e v e ra l
c l a s s e s , th e r e s o lu t io n elem ent i s p laced in th e c la s s which makes th e
l e f t hand s id e o f E quation (31) a minimum. The boundary ta p e i s now
c a l le d a c l a s s i f i c a t i o n ta p e and c o n ta in s th e numbers - 1 , re p re s e n t in g
an u n c la s s i f ie d boundary r e s o lu t io n e lem en t, 0 , re p re s e n t in g an
u n c la s s i f ie d homogeneous r e s o lu t io n e lem en t, and 1 , 2 , . . . . , N r e p re s e n t in g
r e s o lu t io n elem ents p la ced in c la s s e s 1 , 2 , . . . . , N r e s p e c t iv e ly .
I f th e i n i t i a l s i z e o f th e p x p a r ra y fo r c lu s t e r s e le c t io n i s too
la r g e , an incom plete c l a s s i f i c a t i o n o f th e ground scene w i l l r e s u l t . The
com puter program has th e c a p a b i l i ty fo r u s in g th e c l a s s i f i c a t i o n map as
a boundary map, t r e a t in g th e c l a s s i f i e d r e s o lu t io n e lem ents as a lso
27
b eing b o u n d a rie s , d e c re a s in g th e p x p a r ra y to a q x q a r r a y , and
s e le c t in g a d d i t io n a l c l u s t e r s . A ll p rev io u s in fo rm a tio n o b ta in ed on th e
c la s s e s i s u p d a ted , i f a p p ro p r ia te , and th e c l a s s i f i c a t i o n map i s
r e c l a s s i f i e d u s in g th e o ld unchanged in fo rm a tio n and th e new updated
in fo rm a tio n . T h is p ro ced u re can be re p e a te d a s many tim es as d e s ir e d ,
bu t two c l a s s i f i c a t i o n p asse s a re g e n e ra lly s u f f i c i e n t .
Because o f th e la rg e amounts o f d a ta in v o lv e d , th e o u tp u t o f th e
c l a s s i f i c a t i o n map i s nom inally pu t on m ic ro film r a th e r th an s tan d a rd
com puter paper p r in to u t . T his i s ev idenced by th e f a c t th a t th e
c l a s s i f i c a t i o n map from a 70mm a e r i a l ph o to g rap h , u s in g s tan d a rd
computer p r in t o u t , can e a s i l y cover a 400 sq u are fo o t w a ll .
R e su lts a re shown in th e n ex t C hap ter. The poor q u a l i ty o f th e
f ig u re s d e s c r ib in g th e d a ta and com puter r e s u l t s is due to th e
re d u c t io n in s c a le and number o f copying p ro c e sse s re q u ire d fo r th e
p re s e n tin g o f th e in fo rm a tio n .
CHAPTER IV
RESULTS
C la s s i f i c a t io n maps were o b ta in ed from th e a n a ly s is o f two d a ta
s e t s , P u rd u e 's F l ig h t L ine Cl and th e Y ellow stone P ark t e s t s i t e s . The
advantage o f working w ith th e se two s e ts o f d a ta i s th a t th ey have been
e x te n s iv e ly analyzed by o th e r in v e s t ig a to r s u s in g d i f f e r e n t f e a tu r e
e x t r a c t io n te c h n iq u e s . The r e s u l t s o f th e s e in v e s t ig a t io n s a r e m ain ly
a v a i la b le in R eferences 6 , 11, and 12 fo r com parison.
Both d a ta s e ts were acqu ired w ith th e same m u l t i s p e c t r a l scanner
and c o n ta in 12 channels o f d a ta . A ll 12 channels were used in th e
c l a s s i f i c a t i o n , and th e w avelength in t e r v a l s co rrespond ing to each
channel a re l i s t e d in T able 1. The d a ta s e t s c o n ta in 222 tw elve
d im ensional f e a tu r e v e c to rs per scan , and 901 scans from each s e t were
an a ly zed . The d a ta i s a lso u n c a l ib ra te d and th e re fo re on ly c o n ta in s
r e l a t i v e num bers. The s im i la r i ty o f th e two d a ta s e t s d r a s t i c a l l y comes
to an end w ith th e above d e s c r ip t io n .
F l ig h t l i n e Cl i s a v ery f l a t a g r i c u l tu r a l scene approx im ate ly
6 .5 k ilo m e te rs long and 1 .6 k ilo m e te rs w ide, and th e r e s o lu t io n o f th e
d a ta i s app rox im ate ly 6 m e te rs . The ground scene m ostly c o n ta in s
r e c ta n g u la r p a t te r n s o f crop acreag e which appear homogeneous.
28
29
TABLE 1 . ŒAMEL AND WAVELENGTH CORRESPONDENCE
CHANNEL WAVELENGTH INTERVALNUMBER IN MICROMETERS
1 .4 - .44
2 .44 - .46
3 .46 - .48
4 .48 - .50
5 .50 - .52
6 .52 - .55
7 .55 - .58
8 .58 - .62
9 .62 - .66
10 .66 - .72
11 .72 - .80
12 .80 - 1 .0
30
Y ellow stone P a rk , however, i s a w ild e rn e ss a re a approx im ate ly
16 k ilo m e te rs long and 3 .2 k ilo m e te rs w ide w ith a r e s o lu t io n of
approx im ate ly 15 m e te rs . The W ilderness a re a c o n ta in s v e ry i r r e g u la r
shaped p a t te rn s and i s q u i te inhomogeneous in some lo c a t io n s . This
d a ta s e t a lso p o sse sse s a c o n s id e ra b le dynamic ran g e in th e ty p e of
t e r r a i n and amount o f f e a tu re s p re s e n t . For exam ple, th e re a re
m ountains and canyons, and th e v e g e ta t io n coverage ranges from dense
f o r e s t to s c a t te r e d t r e e s , meadows, and f i n a l ly to b a re ro c k s . The
geo lo g ic in fo rm atio n ranges from a sand and g ra v e l b a se , abundan tly
sp r in k le d w ith E lk droppings in th e meadow a re a s , to rock s covered
w ith moss and l ic h e n , and f i n a l l y to la rg e b o u ld e rs .
Cl F lig h t Line
F ig u re 3 co n ta in s an a e r i a l photograph of th e ground scene on th e
l e f t , a boundary map in th e c e n te r w ith th e lo c a t io n s o f th e i n i t i a l
c l u s t e r s , and a c l a s s i f i c a t i o n map o f th e ground scene u s in g s t a t i s t i c s
from th e se c lu s t e r s . The a e r i a l photograph a lso c o n ta in s a l i s t o f
symbols th a t id e n t i f i e s th e co n te n ts o f th e ground scene . The l i s t o f
symbols and th e i r i d e n t i f i c a t i o n a re g iven in T ab le 2. Exam ination of
th e r e s u l t s o b ta in ed from th e m u l t is p e c tr a l scanner d a ta re v e a ls a
problem th a t does no t occur in m ultiband p h o tog raph ic d a ta . The a i r
c r a f t a c q u ir in g th e scanner d a ta was n o t q u ite a b le to f ly a s t r a i g h t
l i n e and had o c c a s io n a l yaw problem s. The scan n er d a ta i s r o l l
com pensated, however, as i s th e case w ith most sc a n n e rs .
The computer maps shown in F ig u re 3 dem onstra te th e f i r s t two ou t
o f th re e in te rm e d ia te o u tp u ts th a t can be o b ta in ed from th e computer
program and a re c o n s id e ra b ly sc a le d down to show th a t th e p a t te r n in th e
31
lu
ID.A.- R
" g
FIGURES. FLIGHT UNE ClA ER IA L PH O TO G R A PH , C LU STER SE L E C T IO N , AND INITIAL CLASSIFICATION
32
TABLE 2 . GROUND TRUTH INFORMATION
SYMBOL DESCRIPTION
A ALFALFA
C CORN
H HAY
0 OATS
P PASTURE
R RYE
S SOYBEANS
T TIMOTHY
W WHEAT
B.S. BARE SOIL
D.A. DIVERTED ACRES
R.C. RED CLOVER
33
d a ta has a d e f in i t e resem blance to th a t o f th e a e r i a l pho tograph . H ence,
i t i s n o t p o s s ib le o r n e c e ssa ry a t th i s s ta g e to be a b l e 't o read th e
symbols on th e com puter maps.
The boundary map c o n ta in s 79 d i f f e r e n t c l u s t e r lo c a t io n s a f t e r
s p a t i a l m erging. A 10 x 10 a r ra y was used to s e le c t th e se c l u s t e r s .
The f i r s t c lu s t e r i s a t th e top o f th e map j u s t to th e r ig h t o f th e ro a d ,
w h ile th e second c l u s t e r i s to th e r ig h t and j u s t below c l u s t e r 1 .
C lu s te r 3 i s th e top l e f t c lu s t e r in a co rn f i e l d , w h ile c lu s t e r 4 i s
th e f i r s t c l u s t e r in th e soy f i e l d below th e wheat f i e l d to th e l e f t of
th e ro ad . C lu s te r 5 i s th e f i r s t c l u s t e r d i r e c t l y below c lu s t e r s 1 and
2 and i s a lso lo c a te d in a soy f i e l d . C lu s te r 6 i s in th e same soy
f i e l d as c lu s t e r 4 and i s j u s t below c l u s t e r 4 , w h ile c lu s t e r 8 i s j u s t
to th e r ig h t o f c lu s t e r 6. The r e s t of th e c lu s te r s fo llo w u s in g th e
same computer p a t te r n lo g ic . Only 43 s in g le c h a ra c te r o u tp u t symbols
a re a v a i la b le to name th e 79 c lu s t e r s and, th e r e f o r e , th e symbol usage
i s re c y c le d s t a r t i n g w ith c lu s t e r 44. T ab les 3 and 4 g ive th e o r ig in a l
c l u s t e r num bers, ground t r u t h in fo rm a tio n , a d e s c r ip t io n o f th e s p e c t r a l
m erging p ro cess and th e f i n a l c l a s s number. Remember th a t when s e v e ra l
c lu s t e r s a re s p e c t r a l ly merged, th e number g iven to th e merged c lu s te r
i s th e sm a lle s t c lu s t e r number o f th e c lu s t e r s invo lved in th e m erging,
and some o f th e rem ain ing c lu s t e r s n o t invo lved in th e m erging may have
t h e i r c l u s t e r numbers changed in o rd e r alw ays to keep th e numbering o f
th e c lu s t e r s in a c o n se c u tiv e o rd e r . T his i s i l l u s t r a t e d in th e s p e c t r a l
m u l t ip le m erging columns o f T ab les 3 and 4 . I f no ground t r u t h i s
a v a i la b le fo r a c l u s t e r , th e l e t t e r U i s used to in d ic a te th a t i t i s
u n id e n t i f ie d . E xam ination of T ab le 3 m u l t ip le merge number 1 r e v e a ls
34
TABLE 3. MERGING PROCEDURE FOR FIRST 40 CLUSTERS
CLUSTER IDENTI- SPECTRAL MULTIPLE MERGE NUMBERFINALCLASS
NUMBER FICATION 1 2 3 4 NUMBER
1 U 1 1 1 1 12 U 1 1 1 1 13 C 2 2 2 2 24 S 3 3 3 3 35 S 4 4 4 4 46 S 3 3 3 3 37 S 4 4 4 4 48 S 3 3 3 3 39 S 4 4 4 4 410 S 5 5 5 5 5
11 DA-BS 6 6 6 6 612 C 7 7 7 7 713 C 7 7 7 7 714 C 7 7 7 7 715 u 8 8 8 8 816 s 9 8 8 8 817 s 3 3 3 3 318 BS 6 6 6 6 619 s 10 9 3 3 320 U 8 8 8 8 821 C 11 8 8 8 822 c 12 8 8 8 823 c 8, 9, 11, 12 8 8 8 824 c 10 9 9 925 s 7 7 7 726 s 4 4 4 427 s 7 7 7 728 w 11 10 10 1029 s 3, 9 3 3 330 c 11 11 1131 0 12 12 1232 0 12 12 1233 c 13 13 1334 w 10 10 1035 w 10 10 1036 0 12 12 1237 u 14 14 1438 w 10 10 1039 c 15 3 340 w 10 10 10
35
TABLE 4. MERGING PROCEDURE FOR CLUSTERS 4 1 - 7 9
CLUSTERNUMBER
IDENTIFICATION
SPECTRAL MULTIPLE MERGE NUMBERFINALCLASSNUMBER
41 C 14 14 1^ 14 1442 U 15 14 14 14 1443 s , c 3 3 3 3 344 u 14, 15 14 14 14 1445 0 15 15 15 1546 w 10 10 10 1047 s 16 16 16 1648 u 16 16 16 1649 DA-R 17 17 17 1750 DA-R 18 17 17 1751 P-0 19 18 18 1852 DA-R 1 7 , 18 17 17 1753 DA-R 17 17 1754 DA-R 17 17 1755 0 19 19 1956 0 19 19 1957 C 8 8 858 C 20 20 2059 C 8 8 860 S 21 21 2161 S 22 21 2162 S 21 , 22 21 2163 S 21 2164 S 21 2165 C 7 766 S 22 2267 S 7 768 S 5 569 S 5 570 S 5 571 S 3 372 S 5 573 S 23 2374 u 1 175 s 22 2276 s 23 2377 s 24 2478 u 3 379 u 3 3
36
th a t th e s t a t i s t i c s o f c lu s t e r s 1 and 2 w ere merged to g e th e r and th e
r e s u l t was c a l le d c lu s t e r 1. C lu s te r 3 d id no t merge w ith c lu s t e r 1 ,
bu t was renamed c l u s t e r 2 so th a t co n secu tiv e numbering would be
p re se rv e d . C lu s te r 4 was renamed c lu s t e r 3 because i t would n o t merge
w ith c lu s t e r s 1 and 2 , and c lu s t e r 5 was renamed c lu s t e r 4 because i t
would n o t merge w ith c lu s t e r s 1 , 2 o r 3. C lu s te r 6 would merge w ith
c l u s t e r 3 and th e s t a t i s t i c s o f c lu s t e r 3 were updated to in c lu d e th e
s t a t i s t i c s o f c l u s t e r 6. F in a l ly , c lu s t e r 23 was a b le to merge w ith
c lu s t e r s 8 , 9 , 11 , 12 and th e s t a t i s t i c s o f c lu s t e r 8 were updated to
in c lu d e th e s t a t i s t i c s o f c lu s t e r s 9 , 11, 12 and 23. The renam ing of
th e c lu s t e r s r e s u l t in g from t h i s m u lt ip le merging i s shown in m u lt ip le
merge column number 2 , and th i s column c o n tin u es u n t i l an o th e r m u ltip le
merge i s en co u n te red . The c l a s s i f i c a t i o n map r e s u l t in g from th e merging
and f i r s t c l a s s i f i c a t i o n pass i s shown on th e r ig h t hand s id e o f F ig u re 3.
T his map c o n ta in s 24 c la s s e s , o r f e a tu r e s , as in d ic a te d by th i s h ig h e s t
number in Table 4 under th e column e n t i t l e d , "F in a l C lass Number."
Because th e c l a s s i f i c a t i o n was in co m p le te , a d d i t io n a l c lu s te r s were
s e le c te d by a 6 x 6 a r ra y s t a r t i n g w ith c lu s t e r number 25, and u s in g th e
c l a s s i f i c a t i o n map as in p u t f o r th e c l u s t e r s e le c t io n r a th e r than th e
boundary map. The merging p roced u re i s l i s t e d in Table 5 under th e
column " F in a l C lass Number" s in c e no m u lt ip le merges were encoun tered .
The com puter program only a llow s f o r 43 c la s s e s and th e re fo re re fu se d to
acc ep t any a d d i t io n a l d a ta a f t e r c lu s t e r 48 , as in d ic a te d in T able 5.
T able 6 l i s t s th e i n i t i a l c lu s t e r numbers o f a l l c lu s te r s th a t a re lo c a te d
in th e same f i e l d f o r bo th c l a s s i f i c a t i o n p a s se s . T his p ro v id es an
a d d i t io n a l check to determ ine w hether th e m erging was conducted p ro p e rly
37
TABLE 5. MERGING PROCEDURE FOR CLUSTERS 25 = 52
CLUSTERNUMBER IDENTIFICATION
FINALCLASSNUMBER
25 WATER 2526 C 2627 C 2628 DA-RC 2729 S 2830 S 2931 DA-RC 3032 DA-RC 3133 P 3234 DA-RC 3335 C 3436 DA-RC 3537 DA-RC 3038 P 3639 C 3740 C 3741 C 3842 H-RC 3043 H-RC 3044 C 3945 0 4046 0 4147 0 4248 U 4349 RC50 RC51 052 RC
38
TABLE 6. MULTIPLE CLUSTER FIELDS
CLASSIFICATION PASS 1-10x10 ARRAY INITIAL
CLUSTER NUMBERS IDENTIFICATION
CLASSIFICATION PASS 2-6x6 ARRAY INITIAL
CLUSTER NUMBERS IDENTIFICATION
1,2 U 26,27 C
4 , 6 , 8 S 3 1 ,3 2 ,3 4 ,3 6 ,3 7 DA-RC
5 , 7 , 9 S 39,40 C
1 2 ,1 3 ,1 4 C 42,43 H-RC
17,19 S 4 5 ,4 6 ,4 7 ,5 1 0
2 1 ,2 2 ,2 3 ,2 4 C
25,27 S
31,32 0
3 4 ,3 5 ,3 8 ,4 0 w
4 9 ,5 0 ,5 2 ,5 3 ,5 4 DA-R
55,56 0
57 ,5 8 ,5 9 C
60 ,63 ,64 S
6 6 ,7 3 ,7 5 ,7 6 S
67,77 S
6 8 ,6 9 ,7 0 ,7 1 ,7 2 S
39
and to a s s i s t in lo c a t in g th e f i r s t c l a s s i f i c a t i o n p ass c lu s t e r s shown
in F ig u re 3 i f d e s ir e d . The reason th a t one f i e l d may have s e v e ra l
c l u s t e r s i s th a t boundary p o in ts w ith in a f i e l d may n o t p erm it s p a t i a l
m erging o f th e se c l u s t e r s . S p e c tra l m erging i s used to overcome th i s
problem .
T ab le 7 l i s t s th e f i n a l c la s s number, com puter symbol p r in to u t and
a b r i e f d e s c r ip t io n o f th e c la s s o r f e a tu r e based upon th e a v a i la b le
ground t r u t h .
A u s e r may now d e s i r e to in t e r p r e t th e r e s u l t s f o r h is s p e c if ic
n eeds, which may be crop i d e n t i f i c a t i o n , fo r example. T able 8 was
p rep a red fo r t h i s example and fo r exam ining th e f i n a l r e s u l t s . C lasses
1 , 7 , D and / a re n o t l i s t e d in th e ta b le because a s p e c i f i c crop name
o r f e a tu r e could n o t be a t ta c h e d . N o tice th a t c la s s e s 7 , D, and / occur
a t th e edges o f th e com puter map.
F ig u re s 4 th rough 15 a re th e f i n a l c l a s s i f i c a t i o n r e s u l t s fo r
f l i g h t l i n e C l, and F ig u re s 4 th rough 9 co rrespond to th e l e f t s id e of
th e a e r i a l pho tograph , w h ile F ig u re s 10 th rough 15 correspond to th e
r ig h t s id e .
In F ig u re 4 w ate r i s re p re se n te d by th e l e t t e r 0 and wheat by th e
number z e ro . The ze ro s have a s l i g h t ly re c ta n g u la r shape as compared to
th e l e t t e r 0. F ig u re s 7 th rough 9 s t a r t to show s e v e ra l a re a s th a t were
n o t c l a s s i f i e d . This i s because th e maximum o f 43 c la s s e s was o b ta in ed
in th e a re a o f F ig u res 7 and 13 and th e rem ain ing u n c la s s i f ie d r e s o lu t io n
elem ents were s ig n i f i c a n t l y d i f f e r e n t from th e 43 p re v io u s ly o b ta in ed
f e a tu r e s .
40
TABLE 7. FEATURE SYMBOL AND DESCRIPTION
CLASSNUMBER
COMPUTERSYMBOL BRIEF DESCRIPTION AND COMMENTS
-1 • UNCLASSIFIED BOUNDARY RESOLUTION ELEMENT0 UNCLASSIFIED NON-BOUNDARY RESOLUTION ELEMENT1 1 UNIDENTIFIED - CLASSIFIED AS CORN IN REFERENCE 62 2 CORN3 3 MIXTURE - 84% SOY, 8% COEN AND 8% UNIDENTIFIED4 4 SOY BEANS5 5 SOY BEANS6 6 BARE SOIL7 7 MIXTURE - 51% SOY AND 49% CORN8 8 MIXTURE -73% CORN AND 27% SOY9 9 CORN
10 0 WHEAT11 A CORN12 B OATS13 C COEN14 D UNDECIDED - PROBABLY CORN15 E OATS16 F PROBABLY ALL SOY -89% SOY AND 11% UNIDENTIFIED17 G DIVERTED ACRES AND RYE18 H PASTURE AND OATS19 ■ 1 OATS20 J COR]H21 K SOY BEANS22 L SOY BEANS23 M SOY BEANS24 N SOY BEANS25 0 WATER26 P CORN27 Q DIVERTED ACRES AND RED CLOVER28 R SOY BEANS29 S SOY BEANS30 T DIVERTED ACRES AND RED CLOVER31 U DIVERTED ACRES AND RED CLOVER32 V PASTURE33 W DIVERTED ACRES AND RED CLOVER34 X CORN35 Y DIVERTED ACRES AND RED CLOVER36 Z PASTURE37 = CORN38 $ CORN39 9 CORN40 f OATS41 ( OATS42 * OATS43 / UNIDENTIFIED
41
TABLE 8 . USER INTERPRETATION OF RESULTS
CATEGORY COMPUTER MAP SYMBOL
CORN
SOY
BARE SOIL
WHEAT
OATS
DIVERTED ACRES
DIVERTED ACRES
PASTURE
WATER
RYE
RED CLOVER
2 ,8 ,9 ,A ,C ,J .P ,X ,= ,$ ,»
3 ,4 ,5 ,F ,K ,L ,M ,N ,R ,S
6
0
B , E ,H , I , ' , ( , *
G
Q,T,U,W,Y
V,Z
0
42> J' ni"
> .•* ."I w"'J* 0 ."* .■' IM JJN * •■>.'.■'O-.’*.'-.'*-.'*• • ........... • a**r* J' Z'C I* J' J' .......................................%•»'!>%.>% > .................. ... njf\j j>
. . . o NfttfUftfafMWJDfOWOTI* WVM\ 1 ^ 1 \ 1. . . o . . . N N M rW M M NN N N NM M D D MNWM '■ > % % > % > .. . , * . . . . M NN fU N N njM NM N W V M niWMNWN"
\ ............................... - r ^ r u jM hi i>ir<ii\iHNHhihie\ir\iNr<ihiHt)ir\i-._ —W .^ IV N W V * • • 'V M N N N N N N W rW N N fV n)'
..................N N M fV n iW W N N M N N ' N rVM NW NNM M NM M NN-
. . . W N N N N M N N " (M'S N NnjN fVM M NI\ll\)W VNW Nf\)fV 'OfWf* M W N fW N N N N N D M N lI f\»Nn*M<\)NNNNm)iVNfVfWMN At* . • • TlVVnVVOWWVOVOVWUlil’*
r<i iVN N W W NA IN N M N W VN fVN N 'VN N N N NN W W M W V M N • • • • 'O'Q'DT) Tt'D'O 'O 'O 'Dll'D'DIKiU* (JUt ••<tftnnnthinthiHhihiritnii\iHhli\iHt\tnrithii\ir nihtr hit\if hth)r<ihiXir\i..................DTi^ 'D 'D 'O II'D 'O 'D 'OUbi w W U w'*W N W N N W VNN N N m *IVN N NN 'VW VfVN N fVW ViV rVhih/VniS- . . . . Vn 'S 'OT'D 'DV'D'D V U D U itU WhiNfihlhihl nj. . . ■ -n 'nD -D U H -D I'D D U D t) WUOlAMNNNNNNWNNNNNfVNW NfVNW VWNfW NNNrWNMNAIMPVfWNM. > • T)'O'D'ODT V O D . ............................niHhihti nr<ihif<tNhif>ifihiriihn\initvNhifiif)jMmnir\if‘ini/\iniivnifiihfn)r . . . . 'OII'D'DD'dd. . . ........................NNWNNNWVNNNNNNNMNNMN'U'VNN'MWNIMfVMWfVNWNrUN • . • . Tttl'D'O'D'OU)...........................................iWN. NNNMMNNNNNWNNNNfVNN'VNfWN'VNNNfVWVfVMNlWrv. • • • 'OtI'DtX ....................hiftt hthitsitiifihinfliivnifi/iwfuhifvr mnir funir rvrvr nt/vivhtniranirii.................... .... ......................................................lyN N N W NN N W N N N N NN N W N N N NnflVM N rU AIW N N 'W NW V'V fV.................. ..........................................W VN NW N NW M W N N IVN N N W VN N N W V M N W VM rV 'M iV W W W ."'.........................................................................WWVAIWWV<VWVWfVAWVAWVW)WVAIWVWNWVA)l\IWWNr\|.».«.............................................................................WNNWMMNNNMNNN'WNNWNNfVWVNMNNrUIV' * * .>•
M. ■ . . ‘DTlD 'T l'O 'D D'D 'OD m '0'D '01I'9'T)1I1I‘0 1 7 9 9 W t r W V O . • « iMU * • •W. . D'O'DTJDll'O'OTJTO'OTJ'O'O'O'D'O'OTJD'O'OTnJTniinj'OIIUwT» TJ. .« U'D'O'Q'O'O'DllD'OI'D'O'DTJ'D'O'O'P'D'O'D'ODO'O'D'OTt'O'S'D'OUU'ablM iW • .T;Tnn;nDT;'av??'0i;3?DDW9V3V?VD9T;v??vrrwwv»w?. w j
. . . ^ . . . Tj-n ■ÜTJ'OtlT) O'OTni'D'BUH'OTJTJ'O'OTI'O'OTJTJDB'OUOU'D'O'OH. ?. J J}J J S. . . Ti. *. Tj ‘D'O'O'c'OTJTnnjTj'oinnjTnnj'OTnjTjTj'DTj'oti'OTj'Otrf uwt»- • • ^............ DDTI'aUTfTfTnflTWWnïFDTîT'DWW????????? . . . . . .. . • ■OUTfBTITJTJTnJ'DTIUTJ'OTIUTnlTnnJTJ'OTJ. "OUTTITI TJU OJ................... C*0 {À* . . . . . . . . . . . . . . . . . . . . . .??3Dq?30*?mnn:???vr(^w3T;T)9w<x <x b*. > o>* . . .* > . • ...................... noD'OTl'nTID'D'O'DTD'O'O'O'D'OU'D'O'O ‘D'D'O'D'O'OUCl. *Oum........................... 0> .'O 'D 'n'S 'O Va'O'n'D 'D D'D 'D'D'O 'D 'D 'D UW OUt^ WW' m ........................... - - 'UU i#w .................. DDOOOÙO'WL* . . . . . . . . . . . . . . . OJQOiS'JOiS'J •
. . . . . . . OOOSOOOOÛO . .
. . aooois-joooij • a j ooaacoaoooo a o o o a j o o o a •
o o o a o o o o o o a o a a • a a o j o o o a o a : ^ ' • aa oaaaaaaa»«.. •JOOÛ aaaoaaoa- • • • oa oooGOoaoooaoiSooa- « • • 'JJOOQOOOiDûaO' • - •
N f*K tw tf*n f»hn^H h inr4h tr< iH h ih tw > inr \iW > it\iN h i W W W AW W AW AM W VNW W VW VfW N N fU IW fW N ' 'W W V W N N M fyN M N N W fV N N W N N N N N N . .Jw).
■WWVWVAlftffVWllWVIVIV'VNMNIUfVfMIV. ..'W #VNNW »*/»f»NW V#VNIVr>f/yhl'« 'VW U •VWWWNNWVNNAWVWVWV « r\>M . . .NWWWWMWIVmWVN'VrxK . Mrs».................M N N N M NM M NM M M M M ................................MNMMMMMMMMMIM" ——M ...............................MWMMAIMMMMMM > ...................................M MMM M MM — ...................................
...................... < <J.......................................A f .D w m w w w w w #^WA(X(W— "«AA A A »*. . . . . O O . . . ....... ...... « . UUUUwiril W». « M t g . A .*««««.# . . . .A A A . . . . . . . <. . . . . . . . A * . . . . . . i
. . . . . . . . . . . A A A ^ » k A A w . . . . O . . . . . .
.................. .«A W W .^w ^»».» ;.A .^.*w *.A A A A A A A A A A A , | A ................................. . . . .
................... "O. . . . bJ » w A l w ................... ......................
. . . . . . . a#».«WM.«#aw.g^s^bi#ÔIWWWÛfW*W&ü»Aw»A&AAAWM..* » i.^M A w w A A A A A A A i.« .^M A t# A ....................................... . . . A » — L»WW LW A.*W AAAW .«.«.'AMW .^AA.^W W W AAAAA#^— .....................................................#^AWl^WWWWWWl.d Wb»ü»Ub»b»AirfAAA A m » A u A A A i^ x —wW n# w —A tmu .......................................A.PA~>.j>aiü<W(<Jll.WUUUb«(AUblOWACrfAAAA>*H>AASH>.::.NiH>{>->*>« . •> MM ......................
. . . . . . . . . . . . A f w.^wALdWWV*. mviW Û»WülW WaAA*f .^ " 'A A "».«i^A . (I : *(riU ^IA s9A U b»^ A« » ................. ...
...........................................A iJ . ........................ O ...ww.* ; t A(W ................................................................... OA . • • «• . • • • AwwWW' AWWHWWWWWtWUfWWWWA"' U . . . . . . . .
........................................................................................ .......................... AUWmWWWWWWAW Au»WWWWWtWU—M.T>. W A A tW lW W n w A ....................
............................................................................................................... :fOHM(Mii/<M(M<j/(M< lM(M' '’iaia<JlMUl(M{MOIUftU/Vn h.W 'T W A A U W A 'T U U SA ...................
.................................................................................................................. " iw w w w w w w w n ^ i 'n 'n w w w w (A i» ^ A u w 'iw A ^ '% . . . . .
............................................................. ............................................. .... il(M<aühO‘*U{M(iHiHjtO/<ÀV(MWCUMUIOt<À'*tViii''IVllOHMi^ùiLllfn<M(AJl WHUk . . . .
............................................................................... . . -. I t. . . WWWWWA. A(XW(WwWWWWWWVCnw?'?W(X&*(AW(XWWW?WWWW;xn(,*A(X . , . . .
........................................................................................ .......................IAWWWUAWUWWWWWWWWWW AW A ....................
............................................................................................................ ilWWWWWWWWWWWWWWWWWWO»iAWsOAWWWWWWWW(AWWAA|OWAAA........................................................................................................... « ..................... wwWWWWO»ÙfWÔr(XtAi*WW^ùfW^7WW^^Ù<W^)WO'^WWO*WW?^kAAA««#»A .^ , . .................................................................................. .................... WWWWWWWWWWWW—A A w W W W L W W üt-. WWW WW WW AA'^U'^ W A. . . ............................« 'I .....................................,-rV ... WWv»WWWWWU»ÜHAWWWAAü#WWAAwWlAA''1WWW(AAvMAWW^Wn'n^ A . . .......................— ........................... o Z ' W W W ti'W W ü'W W ùW AW W W W AW W ^A'nAAAM .W l'nW W W W W W W W ^^I^^'n ^ . . ............................................ w X X x " n w w w w w w (A w u w w w w w n w w w ^ w w A A w ^ A w w w w w w w w w w ^ 'n i ^ i '^ ^ . . . ........................... I. . 0« I . . ' : W W W W W W W wW W W W IW W W W W n^W W W W I'TW W W W W W IlA W ^'n^^TI . . . .
. . n«A A .g .^ w w w w w w iw w w w w w w w u w n 'n 'n w w w w w w v iu iu iw w w 'iw w w w w w u w w iW i^ ^ ^ 'n . . ..*ncA W'DuWtriUWWWWWWbKAUUWCKAWUWIAUKAWWWWUUW'nbMWWUHitWWCii.^UCrfWU . . ............................................... WWWWWU#WWWW«AWWWWWWWWWvyv(«A'AW^W»MWWWWWWWWWWWn^WW''IWAk*AAwW . . .. ....................... ... w w w w w w w w w w w w w w w tA w w w w w w w w w iw w w n w w w w w w w ^ ^ ^ w n iw ^ w A w w A w w n w A - n i . . . . ............................................... w w w w w w w w tA w w w w w w w w w w w w td w w w w "I w i ‘n 'n w i ' ') w u w 'n w '* i 'n '^ ^ '^ w A 'n w u A ^ w u A ''} 'n 'n ^ . . . ............................................... w w w w w w w w w w w uM A W w w w w w w w w w w ow A w w w .................................................................. WWWWWWWWWWWWWWWWWWWWWWWWWOKAWW^^'n^ b»WWfciMWb»;K'n^7t7(A^(A'’l**IW U t«A ''l 't ''V ................... . . i H b A ................... WWWWWWWWWWWWWWWW(WWWWWWW(AWW(AWWl%WV»WW?^'nwW ^ • • . •. . w ' i c A .....................« w w w w w w w w w w w w w w w w w w w w w w w w w w w w n ^ ) ( ^ w w n i^ i w w ^ ^ iw w ^ w w n ''iw i# w u i 'n ''* w • . • . .. . b A ........................... WWWWWWWWWWWWWWWWWWWWWWWWWWWWW'HW'nwWUl WWWWW IW W W W 1 w n W W W l^ w w "H . . .'. . lAbAA............. ... .................................WWWWWIAWWWWWWWWWWWWWWIAWWWWWWW WW?;* UWWùf'’f'T WWOfW(rfWWWW'’MW' A . . . .
I . ......................................... — ...(A w w w w w w w tA A W (A w w w w w w w w w w w w w w w w w n ^ w w ^ % ^ w w w w w w n w ^ ;(^ w w w w w w w w w w ;(w w . . . « .. . n.....................—A A u W tA . . . wWWWWWWWWWWWWWWWWWWWWWWWWWWWWWlXWllWWWWWWWW(AWW^^)((AW(A<#^Wl#WWWWW . . .m a a . . . A rsfA A A A A A A A A A A A iA . A * .................WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWUWWWWWW ^IWWWWWWWWWWWWA %. • ..A A A A M A W A A A A A A A A A A A ................................... (AWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW^WWWWWWWWWWWWWWA . . .
_ W w W b « A > > « A * A A » A A A A A S S A .P .......................................WWWWWWWWWWWW(AW(A(AWWWWWWWMW(/^;fWW(<iW«»WWWtWWWWWWti'WWWWWW(AWWWWWWWWWAw .. . MMM * > > a A « A A A A « A > A A » A » » A A A A AN. wMAAWAAAAAAAAAAAAAAAASA.
M.b. AMMMAAAAAAAAAAAAAAAAA' •« .. .«ww . .
wMMAAA AAA A AA A AA AA A A A A' . •..b.^.. -«MAAAAAAAAAAAAAAAA. A* • ■ .yM^_MA.< A AAA AAAA A A A A A A A.......................W -«AAAAASAAASASAAB...........
A_AAAAAA AAAAAAA....................AAAAAAAAAAAA...................................
-..#'1 Aw .. A A A A A A A A A A A*..................................... W Aw AAAAAAAAA. . . . . . . . . . . ..#WM ww AAAAAAAAA..............................................W M M w w A A A A A A A A . . . . . . . . . . . . X hV Mw ww A A A A A A. . . . . . . . . . . .
Aw A A A A...........................
Vww AAw AAw. . . . . . . .
Ï
. . . wiAWU(AWC«U(AlAIAWWWUU0«AW(AWW(AW(AWW7(A(AW(»l(A(AUWI'*IülWW(A(AW(AWU<A<A(A0»UWWWWül(AWWW> •• • UWtAWUWWCMIAWWWWWWWWUWWWWWWWUKAUlAWWWWWOiW^UWWUbKAWWWWOKAtAUWWUWsAMWWA* • > ‘ . • —iM(M<M(a<Mi0tM<M<MOHMV<M<M(MU<il(Mta<M<Mb/iaUV(M(MI(a(ÀI4UUfaiMlMUUVHa WWWWW^%WWWWWWWW(AWW • > • . . .-wWIAWWWIAWWWWWWWWWWWWWWWWLWWWWWWWWWWWWWWWWWWWWWW^^'nwWnWWWWWWWA' . • .• . • WWW«AWWWWW(AWWW<AWWW(AWWWWW(AWW(A(AWWWWWWWWWWWW1''IWW(AWWWlAli*WWWWWWWWW • • • • . « « (AWWWWW<AWWW(AWWWWWWWWWWWWWWWWW(A(AW(AWWWWW(A;K1?^1WWWWWWWWn^WWWWnAll. A . . . • iA(AWUtAUKAWWb<(A(AWW<AtAUCi»U(AWWUWbtb»WWg»<AW<AtAWWWU;V7(''l(j< W'HWWWWWtAWI llWWni bH « > . • . WWWWWW(AWIAWWWWWWIAUI(AWWWIAWWWWWWlA' WWIAWWWW?cnwWWnWWW(AWWWWWn&Ail WA' > ' . —(A(AWWIAWWWlAWWWWWWWWWWWWWWWWWWW(AWW(A(AWWWWWW(AMA(A'n(AlA'nAWWW»&AA(A • • > . • AWCAWO» ^W W W lA W W (AW W W iAtAW (AW W W W W W W W (AW W (AW W W W W W W ;d'n ''î^'n 'ni^^'?A^A^AAAAAA A. . . • W7*WWU7<0«U(A(A(AWW<AWW(AW(AW(AlAWWU(A;'W(A(AWUW<AUUWWW‘nAU ' A(A' W*A'n 'qAAAAAAAAwU> >
UAWWWAWWWWWWWWIAWWWIAWWWWWW 777(A**^<A IA (A UU U W AA A ^ ^tU 'H W U tA ^'n '^IA A A A A A A AA . . • (AWWWWWWWlAWW(AWWWWW(AIAWWWWWWW^%)(?^3(S W W W W W W A A ^ I^ ^ 'T A W l'T ^ A A A A A A A A A A A . .
. . UW(AWW<AWWWUU»(AWUWWUIA(A<AWWU0<(AWnuU(AWWWn'^WWUU^^'’)^ '^ ''i'1 (A C i» '*1 ^ '^A A A A A A A A A A W • > UtAWUWUWWUWWWWUWWWWIAWWUWUWW^WWCA tA S A IA S A W W (A W n^'n ''I^W W ^'^ ''1^ '^ 'nw A A A A A A ^A i1 . . ............ z* • WWWWWWIAWWWWWWWWWIAIAWWWWWWWWWWWWT'^WUIIA1 WW?''I'^? 1 1 W^??'^^1 (A^AAAAA1|1 (A . , .
........................... XX- . (AWlAWWlAWWWWIAWWWWWWWWWWWWWWWWWWWW 1 ' l*U»1'*l 1 '')'^ ''l''l^ 1 'n''I^AAAA'nAA1AA. . . .. . . . ................ ..... lADWW IAU(A9UI<AW W W W W UW (ll(y<A(AU(AW W W UW OI^*'')*1W W A*'l'nbl^'n '^^'l*'l'nwW '^^'n 'nAW « • • A A A A ................. . . . . . . . AiA. . . WWWWWWUWWWWT" WWWWWW1 ?'TWWAWWW' A«*wA« . . • > 00000« > • • .0AA.."»"«WWiAWWWWi1... WWlAWWWWWZiO—"" • • • 0000000*0 ooooooooooooooooooo . . • .. . . . :* A AA A" —UW« WW«" . . . II. ooooooooooo oooooooooooooooooooooooooooooooo» . • . >. . . . A A. —AAA........ ooo . • « oooooooooooooooooooooooooooooooooooooooooooooooo • . . •. . . AAAAA • XX. . . OOOO 0000000000000000000000000000000000000000000000000*0000. . . .• . . A A AA A A .......... AOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO . . . •:< '?. . AA A A A A A AA> . • oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo . . . .. %. AAAAAAAAAA > . . ooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooo . . . «. . . AAAAAAAAAAA.........OOOOOOOOOOOOOOOOOOOOOOoooooooooooooooooooooooooooooooooooo . . . .
. . . AAAAAAAAAAAwA> • • • o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . . . .. . . AAAAAAAAAAAAA' . . . OOOOOOOOo o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . . . .. D A A A A A A A A A A A A A A>. ■ . . OOOOOOOOOOOOOOO OOOOOOOO OOOOO OOOOOOOOOOOOOOOOOOO o o o o o o o o o o « . . .. . AAAAAAAAAAAAAAA* * > . OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO . • . .. . AAAAAAAAAAAAAAAAA* w • OOOOOOOOOOOOOOOOOOOOOO*OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO* . . • .. • A A A A A A A A A A A A A A A A A A. WWiA OOOOOOOOOO OOOOOOOOOOOO.'OOOOOO OOOOOOOOOOOOOOOOOOO OOOOOOOOOO • . . .. • AAAAAA AAAAAAAAAAAA(A*. ' • OOOOOOOOOOOOOOOOOOOOOO*OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO . . «.• • 'A AAAAAAAAAAAAA AAAAAAA • . OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOo o o o o o o o o o o o o o o o o o o o o o o o o o . . . .. . AA AAAAAA A AAA AA A AA A AAA A A ' • OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO*. . . . .. AAAAAAAAAAAAAAAAAAAAAAAA* • OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO*' OO. o...........AA AA AA AAAAAAAAAAAAAABAAA> > * * OOOOOOOOOOOOOO*OOOOOOOOOOOOO*OOOOOOOOOOOOOOOOOOOO" *o*.................. . .JAAAAAAAAAAAAAAAAAAAAAAA* . . • OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO*OOOOOOOOOOOOOOOOOO OO........................AAAAAAAAAAAAAAAAAAAAAAAAA......... OOOOOOOOOOOOOOOOOOOO*OOOOOO0. AOOOOOOOOOOOOOOOOOOOO* ....................
I lA. . A A A A A A A A A A A A A A A A A A A A A A A AI . . A A A A A A A A A A A A A A A A A A A A A A B A A A A A
• V a A A A A A A A A A A A A A A A A A A A A A A A A A A A .*. V a A A A A A A A A A A A A A A A A A A A A A A A A A A A."
. . A A A A A A A A A A A A A A A A A A A A A A A A A A A A A w . b*. A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A .. .. a a a a a a a a a a a a a a a : a a a a a a a > a a a a a a a a —
. . AAAAAAAAA MAAA 4A A AAAAAA AAAAAAA .Aw A A A A A A A— ' A A A A A A A A A A A A A A A A A A A.«.AAAAAAAAW VA A A AA A A Aw AAAAAAAAA > 'IA A AA A AA AAAAAAAAAAAAAAAAAA
— AM'» A A A A A A —
. lAOOOOOOOOOOÔOOOOOOOOOOOOÔOOÔOÔOÔÔOÔÔÔÔÔOOÔOOÔOOÔOO. O' . . . . . . . . .
. o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o * ......................................• o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o .......................................... O O O O O O O O O O O O O O O O O O O O O O O O O O O O O o o o o o o o o o o o o o o o o o o o * .......................................... 0 **00000 0 0 0 0 00*00000000 000000000000000000000000 0 ............................ OOOOOOOO00000000*0*0*000000000000000000000OOOOO......................................................• ***0**0**** * 0 * * * 0 * 0 0 0 * * 0 * 0 0 0 0 0 0 0 0 * 0 0 0 0 0 * 0 0 * . . . O..................................................... ***** oooooooooooooooooooooooooo**. . *. . . Wii. 1%. . . % V— . . . w. .. . o o o o o o o o o o o o o * * * * * . **. W :. . UW0»7 11 II nil üi;«W1WV^OiA^OO-‘ :».■*■*•■<■».■'ViA*. . OO . . OO*.. o wuwuwwwuwouuusAiAuwwu wu»xoVw(iiAwii»w;<X(Ao»o;<u»x.xArrruüKiuuwwwwuwuuiuwuwowwWüi uww wwooc'wwwwwwowwoowiA;'?:* .
. . AA —
. .. —AA———— .
. ***. « — * A* —»' (A—
. * — A * * —* —
. — — — A * * * * *
. w—
. . *»&**»***
. iAW-»A»A|AA*
. <A«AUIU«IJi W&A. UlblbAbAJI bitAiAiA
. *AVIW»UI»A»AJI»AiAV*
. gib*>AkAUibt<AiAUi<A . UlAUiAUiniiAOIAbl
. . Abla AOIbBlA AUl ■ b«OiUIUIJib*b«b»A.. SAiAUiniiAkAba«A . . lAUdiOtol. U iXZ
. AAA.VAAAAA . AAA.VAAAAA
. W A A A A A A A A . .AAAAAAAAJM A A A A A A A A A A A A A A A A A A A w A . W A U U A r 'A A W U W U A A W A U 0?AW W AW W W W W AAW W W VOW AAW W AAAW AW A O O A A ?
w M A A A A . A MM A A A A A A A - - .AA A A A A A A A A A A A A A A A A A A A A A A A A A A A A ^ A A A W A W W A A A A A A A A A A A A A A A A A A A A A A ;* A ; r ; r ^ A A ^ A.7 rt V . . >w w w w A w M — —A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A T r~ A A A A A A A A A A * « * •
w w w w w —— A A A A A A A A A A A B . A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A r r r * r i~ A A A A . '* A V r ( V t , . .M w w w w A - . .A A A A A A A A A A A A A A A A A A A A A A A A A B A A A A A A A A A A A A A A A A A A A A A A A A . A A A A A A A A A A A A A A A V ? A A A A A J J A X ^ r A A X X * * '> A A-<. >
M w w w w M - - - - A A A A A A A B A A A B A A A A A A A A A A A A A A A A A A A U A A A A A A A A A A A A A A A A U A A A IA A A A A A A A A A 'IA '^ 1 '^ A A A O ;X V ^ A A X A 'T X T . X A A > > WW.WW —M ——. — A A A A A A A A A A A A A A A A A A A A A A A A A A X A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A U A A A 'n V A ^ W X X A A X X X X A A * X ~ *A A A A > • .
O wM —— . —<Ai0A A A A A A A A A A A A U A A A A 'A A A A 'A A A A A A A A A U A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A X A A ^ '^ A A A A '’> ^ A A A A A A A A " . 'A A * A . . .. . — —A AAA AA A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A ^ lA A A A X ^ A A A A A A A A • . A A . • .
- - A A A A A A A A A A A A A A A A A A A A A A A A A A A A A " A A A W A A U A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A ’n 'V A A U A l '^ A A A A A A A A A V ia A V . . . . A A A A A A A A A A A A A A A Z A A A A A A A B A A A A A A A " • • A A A A A W A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A '^ A X A r * X X w A A A A A A A A A A 't . . . .
— — M A A AA A A A A A A A A A A A A A A A A A A A A A A A A A " " ' A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A X A X * " A A " A A " A ^ A O*. . . — — — A A A A A A A A A A B A A A A A A A A A A B A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A X . . 0 0 * 0 0 0 * * 0 * * 0 OO*. . . ,
— — A A A A'A A A A A A A A A A A A A A A A A A A S A ’A'A A A A W A A A A A A A A ( » A A W A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A '’I''1A 0 0 * * 0 0 * * 0 0 0 * 0 0 0 0 . . . , A » A A A A A A V A A A A A A AA A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A W A A A A A A A A A A " n A A A A A A A A A A A A A A A A A " 0 0 * * * * 0 * 0 0 0 * 0 0 0 0 . . . .
- A M A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A W A A A A A U A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 0 0 0 * * * * 0 * 0 0 * * * * 0 * . " • ■ — & — BgU)(XA A A A A A A A A A A X X A A A A A A A A A A A A A A " A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A " 0 0 0 * 0 * * 0 0 0 0 * * 0 0 0 * . . «- * - A B iA A A A A A A A A A A A A A A A A 3 A A A A A A A A A A A " A A A A U A A W A A A A W A A A W A A A A A W A A O A A A A A A A A W A A W W U A A A " * 0 0 * 0 * 0 0 0 0 0 * * * 0 0 ..............M A A M M lfilA A A U A A -A A A A 'A A A A A A A A A A A A A A A A A A i. 'A A A A A A A A A W A A A A A A A U A A A A A A A A A A U A A A A A A A A A A A A A A A A A " 0 0 0 * 0 * * 0 * * 0 0 * * 0 0 ..............
— - M AA W U 'A AWWWWA A'A A A 'A A A A A-A AUW AA-A A A A W tf (/WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW" 0 * * * * 0 * 0 0 0 * * * 0 ............MWW» A 3 3 AAWWWWW A A AW A A A A A B Z X A A B B AAWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWü» W * * * * 0 0 * * 0 0 0 . . . .
"4M UW AB A A 3 A A AAW W A A A A A A A A A A B W 3 A A 3 AAZWMWWlAWWWWWWWUlWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWX " * * * * * * 9 0 * 0 0 0 ...............M MW WMAA 3 3 3 A A A A A A A A A A A A A A A A A A A 3 AAAWWWWWWWWWWWWUWWWWWWWWWWWWWWWWWWWWWWWWWWWWUIWW Xb» * . * * * 0 0 * * 0 0 * * 0 0 . . . ."4MWA A A A A A A A A A A A A A A A A A A A A A A A 3 3 ABAAAAWblWWWWWWWWWUWWWWWWWWWWWUWWWWWWWWWWWWWWW^XWWVWb» W'*?" * * * * 0 * 0 * * * * 0 0 * . • . .
A 3 A 3 A A A 3 A A A A A A A A A A A u r A 3 A 3 A A A A ABBAAWAWWWWWWWWWWUWWWWWWWWWWWWWWWWWWWWWWWWWb» WWWWWWUWiXOO * * * * * * * * 0 * * 0 0 ...............M A A A A A A A A A A A A A A A A A A A A A A A A A W 3 3 3 3 3 . XWAWWWWWUWWWWWWWWWWWWWWWWWWWWWWWWWWWWW P lrfU U U U W U . 0 0 * * * * 0 0 0 0 * * 0 0 ...............A A A A A A 3 3 A A A A A A A A A A A A A A A A A A W W W 3 3 3 3 A B A 3 WWWWWUWWUWWWUWWWUWWUWWWWWWWWWWWWWWWUWWWWWWWWUl" • 0 * * « . * * 0 0 * * 0 . . * . . . . M A A A A A A A A 3 A A A A A A A 3 A A A A A A '3 A A W 3 3 3 3 3 0A 3 A AWWWWWUWWUWWWWwWWWWWUWWWWWWWWWWWWWWWWWUWWWUIWUtW" W. « . A A A A W A A . " . . . .A B A A A A 3 A 3 A A A A A A A A A A A A A A A A A A A A A 3 A A W A A B A " WWW WUWUUWWWWUWWWWUWWW WWWWUUWWCKWWUlAWWWA A 3 A AWb»W A —WW—W AWWA W" W—W— " • . .A A A A A A A A A A A A A A A A A A A A A A A 3 A A 3 3 3 3 B A A A . A 3 " " . WWWWW WWWWWWW—WWW WWWWWWWlAlOWWWWWWAsl). (A—iAU»<AAWWW——— WWWO*WAAWWWWW>W. . > .A 3 A A A A A A A A A A A A A A 3 A A A A A A A A A A A A 3 A A 3 A A A B " " " DWWWWWWWWW A(A A WWWWWWWWlAlPWAWWW^sOa AWsOWWiAA—lAtAiA—— A AWWWWWWW.............
A A A A A 3 A A 3 A 3 A A A A A A A A A A A A A A A A 3 . " . A . " A A 3 A A AWUWWWWWWWAWWiAWWWWWlAWWWld—WWWAlAsAlP—l3U>—WWWIAWW—W— WAWWWWWWWWWWW. . . .WWWWA A 3 A A A A A A 3 A. . . . A " 3 A'A A A A 3 WWWWWMM A A A '3 A ’AAiAUWWUWWWWW’AW WWWa—U» WWWWWWWWW<£»<Al^<^ W (A *W W *— WWWWW —— WWsA—«0 — .................WWWW" 3 3 3 3 . A . • —W. . W A A A A A A A A A A A ’AW A WA" A'AAA'AW W WWWWWWWWWWU7lAU>W WWWWWWWWWWW^WWlAiA WWW A—4) AiAiA 3 * O U }—— — — <A— ...............A -3 3 3 3 3 A 3 A . . . 3 . 3 A A A 3 3 3 3 3W A 3 3 3 3 A A 3 WWWWWWWDWUWWWWWWWWWWWWlAlA* WWWAAlAlflAWWWWWWl^lAA —A ——*A—lAAA iAU )A A —— — ...............w A 3 A A A 3 3 3 A A B B. . A A A D DIMM A D A Bldl.1 0 n n n A AiAi/)—IdWiAWWiA D A——lAiA—lAW—lAiAIWA—-A 3 — — — 3 ——,m A —— — — —— . ,D— . . . .
FIGURE 4. FINAL Cl CLASSIFICATION MAP
SEC TIO N 1
i E S h : : . : :loono..MH IQOOOO . IOOOOQCH.. « • • • . ,
I Î I Î I S ” ! | :
iSSSSSîlJli■ i i i i r
l l l l l i lIS93333S93193eS89ll
c h i
I
h - i:3ii4i:
R l(
s ; :
l i l P. P3PHH
îî îîîîîî î î ’ î ü
l i s
VVVVVVVVV £ VVVVVVVVVVVl l i v
VVVVVVVVV 11VVVVVVVl VVV 1 V
VVVVVVVVl VVI VVVV V .V . .1 VVIVV z VVVVVVVVVVl.. V. .VV111 2V1 VVVVllllVV V . . v i l 1 IV IV VVVVl1111VVV VVV
v : a !3189^14191 . . . . VVVl1VVVVVVV 1 VVVVVVVVVVVV
1111198 3 1 8 8 9 1 1 . . 1 “ VVVVVVVVVVVVVVVVVVVVVVVV1
I
«43334444 ^ r y 3444444 4313144444 1 4443344441444333413
l i i i i«iitlil
443 444444444433 344444434
| ? | î î ; : î ; î î 5î î Uî î ‘, : îîîî4 34443533444
i î P i i4 3444444431
4444 444 H !444 444301 444444400 4444444 . .
4444444 . «i* ' OOOQOOOOOOOOOOOOO
x : 3 : : : i 3 4
• 4 5 3 3 3 5 . . , . , . . , , . . , ,O0
000 000 0 00 0 30 0 0 00 0 'OOOOOOOOOOOOOOOOO'
o o o o o o o o o o o o o o o o *. 0 0 0 30 00 0 00 0 00 0 0 0 ' .OOOOOOOOOOOOOOOO' .OOOOOOOOOOOOOOOO'
. OOOOOOOOOOOOOOOO'
.OOOOOOOOOOOOOOOOO'
m S i
IHHimêWHW IIH H ; IH ( H*; HI ; U i vv* r ***004««««« o ................................o ............................... . . . . . . . . 19991111 11 .1 VI V IV 1 VVVVVVVVl vv vvvvvv. . 19911118 1 8 .4 11 VVVVVVVVVVV V IVVVVVVV
I f l l î i9918899888
iJÎIIIIIIIIII* J x ^ ? H ? ? ! ' " i ? P î " i p i i i i l l l l l i l l !
• • • • • • • 3 3 “ . , . 1 . . ..........................4 3 F . . . 1 1 1 1 1 1 1 . 9
...............
^89838888888
888888888133333________
i i i ri i i i v n | | l l i i ; i p î i
p y î î U Î i ’HIsîîiMii................IS S l §§§§§§§§§§§§ 38 3 ,8 8 8 8 8 8 8 8 8 8 8 8 88888 88
. J i l l l l M l. . . . . JXX 8CXXX • •
. . 1T . 81 . XXX XX . • WWX. .W T X . C .
WWWWWWWWWW. . w ................. . wwwwwwwwwwwwww w.
j||c:93T.S9eVPFPiîTT??Tîïi;• _ 3 . 8 . . 1 . . . F . . . . . . .
. 8 8 8 8 8 8 8 :______
988888888 888 88 - '" -------------
|g||iS|||ii?gh39àà,
l i l i l i i i i i i i i i i i i l i i i i F ” ” ®
.lii. .' “':'a“Süæiissi!ssii«i3KîSK!wù’:i!,w w .................. 1 1 1 1 ( ( 1 WWWWWWWWWWWWWWWWWWWW . . s t ( ( .
.............................1 1 C l . . WWWWWWWWWWWWWWWWWWWWW. (. w . . . W W W .............. C 9 1 .WWWWWWWWWWWWWWWWWWWWW. .
W W l U W W W W W W .. 1 WWWWWWWWWWWWWWWWWWWWW.. ( ( ( .WWWW .W W W U U U U W . 1 WWWWWWWWWWWWWWWWWWW T . ( . ( "
WWWWWWWUUUUUWWWWWWWWWWWWWWWWWW. . .W T W W T 11 s WWWWWWWWWUUUUWWWWWWWWWWWWWWWWW. 1 . T T W T W . . 3 < "
WWWWWW W U U U U WWWWWWWWWWWWWWWWWW I T T . (-■ 1 1 .WWWWWn UUU'JUWWWWWWWWWWWWWWWWWWWW . . T T T l » 1 "
1 1 ( . . W WW. . . WWUUUUWWWWWWWWWWWWWWWWWW W W T W W T T T .t 1 "• (WWWWWW. WWWU WWWWWWWWWWWWWWWWWWT W T T T T T T . - “ “ V
WWWW. .w w w WWWWWWWWWWW W W W W T T T T T T T T T T T T E l- w w w w w . XW U WWWWWWWWWWWWWWT T T T T T T T T T T T T T T T - X I 1 T
WWWWWWWWWWWWWW T T T T T T T T T T T T T T T 1 .....................................................- T T T T T T T T T T T T T T T 1 1 t Z
11 . 1 . . .K K K 3 .K .K 83.
" ' M l ? : ' c c (
8 8 88888888888888888888888888888888888888
}e e8 e8 8 3 3 5 8 8 8 8 8 8 •
388888833 888 883 :
WWWWWTWWW 1WWWWWWWWWWWWWW ww
WTWTW T . .WWWWWWWIWWWW-------------.WTTTWTW WWWTT.W WW
ï l i
ï i j ______T 1ï v î 1 1 1 1 î î î i î î î î ' 4 4
111111111 1111111144
...' i i ; : "■ :: i l lP i l I f iM M i-
t : .COCOOOC•
%o
5
i n
e s
CM
i
I
( ô (3: : V 9 9 "c'
888888988! C88888888! C88888888!, , . ...........' ' l i î l i i ï
44
O O O ' A A " . OO* » • •—JBJ»g ^ r a a g f n n n n n n n n n n n n f ' w w w w w w w w w w w w w m w w w u w w w w w w w w w w w w w w w w w w w w w u w w w w w tw w w tw w m w w c^ A u w w w . •
. . w r * * n - M a n n n n n n n n n n n m a - > w z w w w w w w w w v iw w w w w w u w w w w w w w w w w w w w w w w w w w w w w w w o < w w v iw w w w v iw w w w w w w i. . " w «S'A 'jD j» 'S ' . n n n n n n r t n n - « < £ > z z w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w • •
">«u}' ijiiA»s-B'S'BB’ayt. . nnnnnnrtrtnn* > u x t^ i 'w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w . • &DWXWW A A a n n n n n n n n n n n f w D w w w w w W W W W W W W W W W W W W W w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w iA • •
. . . «..i^ . j ) n n * « j ) * @ j m A n n n n n n n n n n j) . w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w • >n A n n n g j ) b-s n n A A A n n A n n n s w w w w w w w w c .w w w w w D U w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w W ' •
o . . j ) n n j ) A « n n n n n n A A n m . ^ w w w w w w w w w w w w w n rr w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w " • •. . M M M >-A ui"ti)‘: D n n n n n 9 s A n - s n n n n n n n A A n w w w w u w w w w w w w w r rz w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w t* « •
. . i* M M " i" A " U - s n n j» A A « - I A ' ■ « 'S A A A A A A A A A ' *W WWWWWWWWWWWWWWDW WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWtA • •.................. M.^M'jB"xUW gB0B'S’A A A > .B n A g B A A « J> A n n A a 3 . Z5\D{DUWWWWWrWZWW WWWW WWWWWWWWWWW WWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWW" ' '. . . . ^ M M " - * " " ( 0 J> -JïS « ‘JB'J>’S 'J )A A A n « J» 'J> A A n A A - • • a % D (x w w w w w rr ZWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWUWWWWWWWWW- 'a . . . BBBOSBJisnnnnsBBnnnrin- ■ <aj»> 'n 'D /~ w w rr '/~ w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w i •. . . M ">«M "-B ""0»J>90B J>a'-:DJ>.SA A 'A .D A ’J b « A A n n A A A « • T r r w zw w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w > •. . BBBSBBBBn j» 3 3 A A A A A A A A A A " ' • rZrwWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWIWWWWW»' • •. . • w z*D Z w w w w w w w w w w w w w o ‘.iw w w w w w w w w w w w w w w w w w w w w w w w w w w w w w w ^ 'n ;« w 'n w a . . .
A A A A A A A A A A . B‘ w o w z w w w w w w w w w w w w w w w w w w w w w w o w w w w w w WWW WWWW w w w w w w w w w w w n "n w ^ :« w wA A'A 'A '9-AAA-AA'AA A A A A A A A A A . A. 7WWWWWWWWWWWWWWWWWWWWWWWW«(0WWWWWWWWWWWWWWWOfWWWWWWWW nWPtWWWWWW" '
. . . . . . . . . . . .M A A A A A A A A A A A A A A A A A A A A A A A A A" ■ ' WWWWWWWWWWWWWWWWWWWWWWWWA WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW- .M M " " " " A A A A A A A A A AA A A A A A A A A A A A A A A A . • A A AWWWWWWWWWWWWWWWWWWWWWWW(OlA WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW • M M " " " S « - A A A O A A A A A A A A A A A A A A A A A A A A A " A " • WWWWWWWWWWWWWWWWWWWWWWWAlgWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWlWWW. • M M " " " » , , .A A A A A A A A A A A A A A A A A A A A A A A A A A A . > WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW. . M M " " », a A A A 'A 'A A A A A A A A A A A A A A A A A A A A A A A . WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW" . .
M " M > -w " A A A A 'A A A A A A A A A A A A n A A A A A A A A A . A WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW* • •. M A " , - A A A A A A A A A A A A A A A A A A A A A A A A A A A ' WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWH . . m m m m m A A A A A A A A A A A A A A A A A A A A A A A A A A A A A > WWWAWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWlW. . " M " , . A A A A A A AA A A A A A A . . . A A A A A A A A A A A ' . WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW^^^WWWWWWWWWWWWWW- * . " A M S A A A A A A A W A A A A A A A A A • . A A A A A A ' A* AAWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW^TWWWWWWWWWWWWWW" • . A A A A A A A A A A A * W AA A A A . i" -AA A A A AA A * • A A WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWWW. >
M A A A A A A A ? W A A A A A A AAAAAAAAAAAAAAAWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW^WWWWWWWWWWWWW • • •4m W AA A A A A A A A A A A A AAA* AA AAAAAAAAAAAA,AWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW7 WWWWWWWWWWWWWWWWWWWWWWWWWWW'*). •M W " " A A A A A A A A A W A A A A . > . AAAAAAAAAAAAAAAA"WWWWWWWWWWWWWWWWWWWWWWWWWWWWW;0*WWWWWWWWWWWWWWWWWWWWWWWWWW • * > .« " " S A A A A A A A A A A A A " * A A A A A A A A A A A A A A A A • WWWWWWWWWWWWWWWWWWWWWWWWWWWWW^WWWWWWWWWWWWWWWWWWWWWWWWWWW* • • m m m a A A A A A A A A W A ' A A A A A A AAAAAAAAAAAAAAAAWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW WW. . " " " A A A A A A A A A A . • ' A A A A A A A A A A A A A A A A A A A A " WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW . • " M " " A A A A A A A . A" • A A A A A A A A A A A A A A A A A A A A A A . WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWUWWWWWWWWWWWWWWWWWWWWW* WWWW 9 . • H " " " A A A A A A * * A A A A A A A A A A A A A A A A A A A A A A AWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW'D'T) W'Tl* > M .^ M " f * j» A A A . . . A A A A A A A A A A A A A A A A A A A A A A A AWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW TIWW. TIWW. . .
W A A A A A A A A A . AAAAAAAAAAAAAAAAAAAAAAAAAWWWWWWWWWWWWWWWWWWWWWWWWWWWWAAWWWWWWWWZ“nwWWWWWWWW.........................................._M A " A A A A A . . . A A A A A A A A A A A A A A A A A A A A A A A A A TWWWWWWWWWWWWWWWBWWWWWWWWWWOTW' WWW" WW" U ' .........................................................................4 A A A A A A . " A A A A A A A A A A A A A A A A A A A A A A A A . . WWWWWAW WWWWWAA A AW'DHWWWW? " I .....................................................................................................................•4 A A A A A A A * A A A A A A A A A A A A A A A A A A A A . AA» . W WWWZP. Z Z W A A '
4 4 4 A A A A . A A A A A A A A A A A A A A - " " 4 4 A A A A A . A A A A A A A A A A A A A J _ m " 4 4 A A A A A . A m A A A A A A . . A ' . . . 4 M " A A A A A A A A A A ' W A. . . . . . . ." M " A " A A A WAWZWAWWW. . . . . . . . ._ " 4 . A.AWNWWAAW.
w "W W WWW. AWWA _ A AWWWWW wwr*<A A A ZW* A9W A W .AA-4-49M W A AW."I
A 4 W W A A W SA _ A A A A A AAAAW W
A A A A A A A A S ' •
WW. . . Dwwr".......................................................... "WWWW WWWW r~ i~ • • •................... WW. A A . AWWWWWWWWWWWWWWrW . .
. W'H AAWW. W'OWWWWWWWWWWWWWWW* w ^ ' .A ,s . A W WA r AWA. WWWWWWWWWWW W* .z r w w w WWW A w w w w w w w w w w w w n w w z :^ .. r . . W W WAAWAAWW AAWWWWWWWWWWWWWWWW . . . . AAAAAW W W AW . . WWWWWWWWWWWWWW
. . . A A A A A A AAA* WWWWWWWWWWWWWWWW ", . A A A A A A A A A WAAW • WWWWWWWWWWWWWWW^
A A A A A A A A A A A W UW W Z' WWWWWWWWWWWWWW?^ A A A A A A A A A A A A A A WWW* ' WWWWWWWWWWWWW?A A A A A A A A A AAA A AW A. . WWWWUWWWWWWWW?
' A A A A A A A A A A A A A A A A rWWWWWWWWWWWWWWW?1 A A AA A A A A A A A A . AAWW. • * WWWWUWWWWWWWW? . •
4 A A WW W A A A Z J . A A A A A A A A A A A A AW U Wl'WWWWWWWWWWWWWW W. • ■ > 4 * W W W A A A A W - i~ ' A A A A A W A A A A A W W WU/~" ' WWWWWWWWWWWWWWW. ' ^■ 4W W W W A A W W W IW . . A A A A AAWWWWWZW U W ? WrWWWWWWWWWWWWWWW •^ m w A w w w A w w w w r- A A r r - r w w w w w w w z z w u w w r r w w w w w u u w w w w w w w w . •^ B w AWWWA WWWW’' A A C ,- ,- WW W W W W W I 3 W U W U ^ W W W W WW W W WW w w w w w .H 4AWWWWWWW A i w w r r AW AWWWZZWWWW- ZWWWWWWWWWWWWWWW
A A AWWW. A A A W A A WWWZ WWW" > WWWWWWWWWWWWWW? ' UW W 4 A A A A A A A A A A A A A A WZWWWW i~2>~WW- WWWWWWWWWWWWWWWW
4N W W W A A A A AAA A AA AAWW ZW r r WWWW ZWWWWWWWWWWWWWWWW- .4 4 WW AW A A A AW WWW W Zi~ W 3 WWWWWWAW . WWWWWWWWWWWWWW?. .
4 4 WWWWW A AWWWWWWWWWWf'- W'^ZWWWWWWW WWWWWWWWWWWWWW^O' .W MWWWWAA WWWWWWWW r r * - : ~ WWWW WWWW WWWW WWWWWWWWWWW . . . .
M 44W W W W W A w w w w w w w r r r r % rw w w WWWWWWWWWWWWWWWWWWWW??. . 4 4 W S A WWAWDWWWWWW i T T . A W W rZ AWWAWWAW WWWWWWWWWWWWWW ?W WWWW A WWWWWWWW WW w r - r~. . . I . WWW wr~ • WWWW WWWWWWWWW w
WA WWWW AAWWWWA AAW W I Z r w WWWW ZZWWWWWWWWWWWWWWW?"?. WW*"W4 A A A A A AWWW. . Z W W W ~ ~ Wr~ i~i ' W 2 ZC> Z ZW r . WWWWWWWWWWWWWW??. WWWWZ A A A A A A W WZ. W W W r W W 3 W A . WWWW. WWWWWWWWWWWWWWW??A W W W A AW AAAAAAAAW W W W r r < ~ Z W- rZ Z W W W W W Z ' WWWWWWWWWWWU-u u w u . . WWW A A ww WWWWWW z I ' r t - w r z z z z w r w ? z . w w w w w w w w w w w w w ? * u u w w w w w w w w z w w w w u w w u z r r r r - r r z Z w Z w w Z A A . '~ w w w w u w w w w w w w w w > w WWWW w w w w w u WWWW w w w w w n j r . . . w w w w w w w w w w w w w ? .WWWWWWWW AU WWWWWWWW W Z '^ ' z w w w Z w w w w u w w w w w w w w w ? ? oWWWWWWWWW w w w w w w w r w z z r u a w <~w . w w w w w w w w w w w w w . . .WWWWWWWWW w w w w w z z r w z r . a a a w w r w w w w w w w w w w w w w . < .WWWWWWWW WWWZ. r* r - r- . r i - r r AA u r w WWWWWWWWWWWWWW W'w w w w w w w w Z w w z r r r r . .- rw > ~ A a w Z Z Z w w w w w w w w w w w w w w 1w w w w w w w w WWWW r r r • w w a a w r z w w w w w w w w w w w w w u ?WWWWWWWWW w w w w '- r r . r - . r- z r~ I'rrZZW W W W W UW W W W W W W W W ? . WWWWWWWWWWW z z w z w r i - . . . a w w . - r r r r w r z . w w w WWW w w w w w w w w ? . mifl WWWWWWWWWWW Z Z w r r- . w r r r r r r z w r r w w w w WWW W w w w w w w w w -
. . oodooooojijoijjo• • o o o o ü c o o ü a o o u i a . «OOOOOOOOJüÜOUU* ' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . o o o o o o o o o o o o o . . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . OOOOOOOOOOOOOOO . OOOOOOOOOOOOOOO . OOOOOOOOOOOOOOO. . o o o o o o o o o o o o o o . . . o o o o o o o o o o o o o• • o o o o o o o o o o o o o o . . o o o o o o o o o o o o o o . . o o o o o o o o o o o o o o ' . o o o o o o o o o o o o o o ' . . o o o o o o o o o o o o o ' • o o o o o o o o o o o o o o.. OOOOOOOO OOOOO . . ooooisoiooooooiDie. • • 0.900000000000 . . Ol9i9(9Oi9(QO19Oi0Oi0i9 . * OOlCiOOiQOlQOOiQOOO ' . OOOlQOOOcOOOtOlOiV.O « • (9Ol9OOOl9Oi9Ol9l0LUi9 . . I9l9l9l9l9l9l9l9t0,0i9l9.9>9 ' « >/»9(9i9(9(9(9i9<9i9i9l9iPt9 . . l9k9t9C9t9l9l9l0«9l9l9iD . . (9 l9 0 l9 L 9 l9 0 t9 l9 0 l9 0 i9 ' « 0 0 ;9 i9 l9v9 i9 i9 l9 i9 i9 ,9 l? 1• • . ,9i90i9l9l9i9i9l9i9i9.9. . . I9l9l9l9l9(9l9t9i0,9i9.9. . . i9i9i9t9l9i9l9l90i9lQ.9.9 . . . .9.90 g,90l9«9i9.900.9 . . . .9000.900.9. .. . . .9"«9 ....
....................IIIII. . 0 0 0
. . . 0 0 0 0 0 0 0 0 0 0 • . 0 0 0 0 0 0 0 0 0 0 0 0
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
• o o o o o o o o o o o o o o . o o o o o o o o o o o o o o . o o o o o o o o o o o o o o . . o o o o o o o o o o o o o . . o o o o o o o o o o o o o• . o o o o o o o o o o o o o . . 0 0 0 0 0 0 0 0 0 0 0 0 • . o o o o o o o o o o o o o. . JO O O O O O O O O O O O• . o o o o o o o o o o o o o• o o o o o o o o o o o o o o ' o o o o o o o o o o o o o o ■ o o o o o o o o o o o o o o . o o o o o o o o o o o o o o . . o o o o o o o o o o o o o • . o o o o o o o o o o o o o • . o o o o o o o o o o o o o . . o o o o o o o o o o o o o
444-1-I-144" - 4444444""44
4 < " 4 4 4 4 4 4 4 4 4 4
A r w z r r z z z w w z z z w z i-
WWWWWw w w w w WWW.. WWWWWWWWWWWW . . .. WWWWWWWWWWWWWW..' w w w w w w w w w w w w w .. .
WWWWWWWWWWWU?.w w w w w w w w w w w w w ..WWWWWWWWWWWWWW- WWWWWWWWWWWWWW.. WWWWWWWWWWWWWW..
' w r WZZWWWWWWWWWWWWWWW?. r r w z z z z w w WWWWWWWWWWWWWW" r r ZrrZZZW W W W W W W W W W W W . . W"
z r z z r r w w w w w w w w w w w w A . . - . r w z r j z z r - w w w w * w w " - •••.• . ii
WZWWZ* WWW.
u w w w w w w w w w w Z Z r r r r r WWWWWWWWWWW . w r w w r &WWWWWWWUUW z r r Z Z w w w w w W W W w u w w r r r . r r - w w w w w w w w Z WW" r . . w w w w w w w w z u r . . w w w w W W W w w r r r r . . . r w w w w w w w w r r r r r . Z r w w w w w w w w 3 r r rWWWWWWWWZ . .w w w w w w w w . w r r .WWWWWWWWZ w r r z r u r . .w w w w w w w w r . w r r r r r w r r w w w w w w w w z r . r . . w r r r r r r w u w w w w u w w r r r r z z r r ." 2 rw w w w w w w w r r r r w r r r r z rz w w w w A W W W W A -w w w w w w w w r r r w r r r z z ....................... WAWWWWWW-w w w w w w w w " u z z r r r . . . . A. . . a a a w w w u w w w w . . w w w w w w w w Z Z Z . Z Z * . WWA A. A "W WWWW WWW WWWW* . w w w w w w w r w z - . WWWAAWAOWWWWWWWWWWWWWWW* ' . . W w w w w w w w w w w w . AW Z WWWWWWWWWWWWWWWW . . "WWWWWWWWWWWAAWUWWUWWWWWWWWWWWWWWWWWW. .\ . WWWWWW4 wwwwwwwwWWWWWWWWWWWWWWWWWWW. .
4 . WWWWUUWWWWWWWWUWWWWWWWWWWWWWWWWWW' . — —4 S >. WWWWWWWWWWW WWWWWWWWWWWWWWWWWWWWW.
4 V 4 S n WWWUUUWWWUWWUWWWWWWWWWWWWWWWWWW.\ N W S 4 'vW WUUUWW WUW WU WWW WWWWWWWWWWWWWWW-N N N N N N N WWWWWWWWWWWWWW WWWWWWWWWWWWWWW- . —S N N N N S N WUUWWWWWWWWWWWWWWWWWWWWWWWWW- B ‘N N N N N N N N NUWWWWWWWWWWWWWWWWWWWWWWWWWW- . .N N N N N N N N N UWWWWWWWWWWWWWWWWUWWWWWWWW- • -----...N ' . n n s n n n n WWWWWWWWUWWWWWWWWUWWWWWWWW- . M N N N N N N N N N N N WWWWWWWWWWWWWWWWUWWWWWWWWUWN N N N N N N N N NsWWWWWWWWWWWWWWWWWWWWWWWWWW- - . - . - . - . - . — - . . .M . NNNNNNNNNNWWWWWWWWWWWWWWWWWWWWWWWWWWW- . —NNNNNNNNNNUUWWWUWWWWWWWUWWWWWWWWWWWWWW- —NNNNNNNNNNNWWWWWWWWWWWWWWWWWWWWWWWWWWW- nN N N N N N N N N N w w w w w w w w w w w w w w w w w w w w w w w w w w w - .N N N N N \N N WWWWWWWWWWWWWWWWWWWWWWWWWWW?IW:N N N N N N n AWWWUWWWWWWWWWWWWWWWWWWWWWWWWWWW NNNNNNAWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW?
AWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW..
. 4 4 4 4 4 4 4 4 . .
♦ . 4 . 4 4 4 . " - —flLI WOU
II r t i i i in n m n . . . . :n : nnn-'ii- ' un. . .I S . - ; n n n r i i i . .1 . .: : s p i i in : iH n n n n .1,m : “ i n n * jn r iP î i i /I
II s n i i I I I I I I n n m n u n n n n ■■n i/r7nn/i-'7.'V/t fi r/in/ : : s : pj. n f in n iirnu n — :pi II. Pinnnnii n . MM finIIm II ii
mm. mm . u umm m m u . . . n
m. . m m. . .
sm mm — m mmmmm-V . . « fummmmmmmmmm m mm m mm mnm m
s : M : m—m mm m mmmmfimmmmmmmmm m um m —-;-->-::-mn : * ••nn m mm m mmmmfimmmmmmmmmmmm m. . - -v-N :m m : : -X- m 11 mmmmmmmmmmmmmmmmmmmmmm. .
> -N->mmmmmmmmm-:> mmmmmmmmmmmmmmmmmmm. . . mmmmmmmmsmmmmmmmmmmmmmmmmmmmm
N N N N N WWWWW WWWWWWWWWWWWWWWWWWWWWWWWWWW. . N N N N N AWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWZ. . - •NNNNNN4WWWWWWWWWWWWWWWWWWZWWWWWWWWWWZZ* — NNNWWUWWWWUUWWWWWWWWUWWWWWWUWWWWWWWWZW—— w N N w w w w WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW1 :> NN w w w w u u w w w u w w w w w w w w w w w w w w w w w u w w w w w w N WWWUIWWWWUUWWwWWWWWWZWWWWWUWWWWWWWWWW WWWWWWWWWWWWWWWWWWUZZZWWWWWWWWWWWWWWWW?W I WWWWWWWWWWWWWWWWWWWZZWWWWWWWWWWWWWWW W.N W W W W W W W W W W W W W W w w w w rzw w w w w w w w w w Zw w w w w i- N w w w w w w w w A u u w w w w w w u z Z w w w w w w Z w w Z Z w w w w r r
mm 11 mmmmmmmm m mm fim mm fim mm m mm mm m mm m . ." - m m m m mm mm m mnm mm mm m mm m mm m mm m mm mm ..
I--.- :. m m m m m m m m fim m m m fim fim m m m m m m m m m m m .. mm. .I. . . , . ,» ,» , .- .— .^ m mmmmmmmmmmmmmmmmmmmmm. m m .. . • . .
m ---------- : sm m m fi :m im m m m m m m rim m m fim m m m m m m m mm..............sm—' m m m fim m m m m m m m m m m m m m m m fim m m m m m m m . ....................
— - :-:,--m m zm m m m m m m m m m m m m m m m m m m m m fim m m m m m m m m m m ..................: î " " .m m m m m i mm zm m m m mfim mm m mm m mm m mm fim mm mm m mm m mm -
: m m wm — ------------------------------------ ------------------------------------------------. - . - .m m %-mmmm ••mmm 1.W " . : m smmmmmmmmmmmmmmmmmmmmmmmmmvmmmmm. . . . .
: i . 1 mm m mm m mm mmmmmmmmmmmmmmmmn-. mmmmmmmm m — . . . i —m z 1 xm m m m m immmmmmmmmmmmmmmmmmm v mmmm mm mm m m-.—. . . . m m m i m m m m fim m m m m m m m m m m m m m m /ifim m m -*--m mm m mm m mm . —. . . .
ZW i w mmmm : m mm zrnmmmmmmmmmmm —m m m m m u mm ............... m m-:.-mm mm mm mmmmmmmmm m m m fim m m —mm. — ..............
Z Z Z Z • : I z m mmmmmmmmmmmmmmmmmmmm —. m . •z i z z z z z -;.-m m zxzzzm m m m m m m m m m m m m m m m m m — .
XXX z z z z i m m m z z z fimmm m mm mm m mm m mm m m — — . .i x z z z z w -m m m m . z mmmmmmmmmmm. mmmmm—— .
w w w w w A A A w w w w w w w w w z z z w w w w w w z z z z w w w w r r z z z z z z z z z z w m m - - m n mm. z z m m im m m m m m m mmmm— mmmmmmmmm w w w w w A A W A A w w w w w w w w w w z z w w w w w z z z z z w w r r r . i x z z z z z x x x z z x x - •- z z z m mm m mm m m .m m m m m m mmmmmmmmmm
n n w w w w -a w w A A w w w A A w w w w w w z w w w w w z z z w w x w i-i- x z z z . T Z Z Z Z z m:'.- m-:— m m zzm mm m mm mm m mm m mm m mm m m —mm— . mm.N w w w w w w w A w u w w A A w w u w z .T Z w w w w u w z z z w w WW- x i i z z z z z mmmmmmmmm m mm mm- mmmmmmmmmm —m m m m m m m m m m ..................N w w w w w w id w w w w w w w w w w w z w w w w w w w w w z w w w w w z z z x x z z z X m z .-m-.-'.vmmmmm xmmmm mm mm m mm m —. mmmmmmmm mmm- . . . N s w w w w w w A w w w w w w w w w w w w w z z w w w w w w w w w w w w ? w i z x i z z i z x z - :-..-mmmm m m m - m - m - mmm -m m m m m m m —mmmm
.. iw w w A A w w w w w w w w w u w w w r z w w r z r w z z w w w w w w w4WWWWWW WWWWWWWWWWWWWWZZWW Z Z Z Z Z Z W W W W W NWAWWWWi «WWWWWWWWWWWWWW rw w w w zZ Z Z Z W W W W W *N N N N W w w w w u w w w w w w w w w w w w Z w rz w z z z z w w w w w ?N SA W W W W W W U W W W W W W W W W W W W W Zl'W ZZrZZW ZZW W W W ZW
W n W W W W W W UW UW W W W W W W W W W ZZZZZZW ZW W ZW W W W W r?1 4 n WWWWWWU'jIWWWUWWWWWWWZZZZ WWWWWWWWWWW m N WWWWWWWWWWWUwwwwWWWWZZW WWWWWWWWWWW-X N WWWWWWWWWWWWWWWWWWWZWWWWWWWWWWWWWWW-. 1
z z z z x x z m m fim m m m z —m — —m :m . — mmmmm— mmmm. m- . - . .z z z x z m mmmmm-:.- ■ m mm mmm — mmmmmmm mmmmmm . . . .z x x z m mmmmm m — . ... mmmmmmmm mmmmm—mmmm—mmmmmmm . .
z . m mmmmm mm..-mm . — mmmmmmmmmmmmmm m u m m m m m u ..m mm mmm .,-mmm -.-m « mmmmmmmmm zm m m m mmmmmm 3
n m z z nnn——nnnr7 inn .-mmmmmmmmm mmmmmmm mmmmmm o x c * .. m m z x T X m. . . mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm—. . . . xm z z x m . . - mmmmmmmmmmmmmmmmmmmmmmmmm—mm— ...........................
m z z z z - . . . 4 . . m mIImmmmmmmmmmmmmm mmmm mmmm— — . . .
FIGURE 6. FINAL 01 CLASSIFICATION MAPSECTION 3
45
. wwwwwWWWWWWWWWWWWWWWZZW WWWWWWWWWWW* XV WWWWWWWWWWWWWWWWWWWXWWWWWWWWWWWWWWW*« ^NN w w w w w w w w w w w w w w w w w w w w rix w w w w w w w w w w " . *n* ^WWWWWWWWWWWWWWWWWWWWW^- /"WWWWWWWWWWW . XXraraïssasaaaaasaaaasSrPîiïïasaaaaaaaaa- ixiîix•• «4* WWWWWWWWWWWWWWWWWWXXXXWXWWWWWWWWWWX XXX XXX t WswwwwwwwwwwwwwwwwwwwwiwwwwwwwwwwwwwwwxxxxN*4W WWWWWWWWWWWWWWWWWWWW WWWWWWWWWWWWWW'
^ WWWWWWWWwWWWWWWWWWWWWWWWWWW" WW' t •N .«—wwwwwwwwwwwww* WWWWWWSZ* ..........—WWWWWWÛ7WUWW' • • • • o . * *—UAAW*** • ' * '
I - m mmmmm m m o m n » —• .... ....n m m mmm *m m m «mmmmmmmmm xm m m m
fTj rn I X »m m ~ -.m m m m » mm >» mmmmmmmmm m mmmmmm
(Tj j j n * . . . H • * mm II mmmmmmmmmmmmmm mmm m mmmm— *— * . * ...........................
u x x x x * • ' «»mmmm m m m x u n mmmmmmmmm* mm* m* —• • * * * —m* . * . » • • . .x x x x * • -> * * mmmmmmmmm • * m m iim m m m m » . . —. n * • • • • • • • * * * * • • • •
«».»« mmmmm* mmmm* xm * • • cou* . . * * • • * • . » • • • h * • • * • * mm* * w w * * . . m **m m n* • • • • m* * * * . * * —* w w ii* mm ——* ————. . ..m. —* . " . « . . . nj* * • H* * * — * Il m —— . !*— m . * . ........ ......... w w A w —* * w m — —(g— — —10— —— —* * ■ • •• • > WWW* W' • • 9 A A — (0— f — — — — r*— H— — — — — >*—* « a *
. W WWW lO* WZ®*Oltf— — —— — — —— — — * • a
. WWWWWWi lHWW®WÜ)Ü)———(0— — ——WWAW—"*—**— — — — — a — — — — — — a * • a. . . . . . . . ww* ®W* . (O9ld'89O)«O(0l£AW — ig— — > ? WW —— — «g— H>Am— — — — — — — ................
^ ................................................... WWW®* WWW#® # # # # # # 'y s # ® ® # ® ® ® # ® w ® ® * O iD —*0® # ——w — — «wm m w A m m yj— — — — — —— • a* « .. . OO* o ........................... —. . • WWW* ® # ® # # ® —# ® ' * # ® # # # ® # ® ® w ® ® # # ® ® i g —® —a m m x ? w ^ m m * —« — — — — — —« «». ...............................WWW* —w w ® z » * ® * ® # # ® ® * * ® ® ® ® ® ® * ® ® ® # * * # ® * ® ® '^ ‘ *®®®‘*'®‘®'®'®^"^ • u>—m m w w « o m ? ' * — «A — — — — — — — w ——«*—« * *
. ^ M—— —. . .« W ® ® ® # » » » ® ® » ® ® ® ® ® ® ® * ® ® ® ® * * ® ® ® ® ® ® ® ® ® ® ® ''* ® ® ® ® ’' m m w w w iô— y>— ig w* — — — — — —— — — — — —**. . . ..«M—————— • • w w » ® ® ® ® » ® ® ® » » » ® ® ® # ® ® ® ® ® ® ® ® ® ® ® * " * ® ® ® ® ® ® “ W®®——w m m w w w m ^ w a a A m w w w w w w ii a —a h a a w ** —— . — a . . .
—— —. w w ® # ® ® ® * ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® #® ® «o # ® io ——w * WWWWWWW7WWA#— icw w w m m w iD — A A w A m w a a — — — . . . .. w $ * @ $ * .* * 3 a < 3 ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® w ® ® ® ® ® ® ® ® ® — WWWWWWWWWWW—# w —m w w A — —<,)io———ilw m m w •»——a —i p a — • . .
M M—. . . —9 « 9 - jB 9 9 9 g }9 -9 '3 ® 9 ® ® ® ® ® ® ® ® ® # ® ® ® — ® # # y ) # # ® A —wm UWWWWWW w w w o o # A WWW#—— — — — — m A w m m #w — • . a a. . . w w ® ® ® ® ® # ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® w ® # w w # # ® ® # # A w w w w w w w w w w w w w — AWWWA—* * — — - —A * m wA m m m w • m—
. . . . , W 9 9 9 9 .3 9 9 9 9 9 ® ® ® # ® ® ® ® ® ® ® ® ® ® ® ® ® ® ® # # ®#®9##WWWWUWWWWWWWWWA —W—— W # — mW'
. . . . . . I . D 9 9 ® 9 ® ® ® 9 -.- i 99# ® ® ® # # ® ® ® ® ® ® ® # 9 W W W W W WW99#WWWWW WWWWWWWWW II mwWW # <>W. . ® ® ® ® ® 9® 'X .®W" ® ® 9 9 ® ® ® ® ® 9 # ® # ® # w — WW7—O # ——WWW m w w w w w w w w D w w w w m m w w w w
—— . . . w ® ® ® ® # ® ® ® # ® ® ® ® ® # ® z ® ® ® # # ® # ® # ® # —w z # # # # # w w w ;f^ w w w w w w w w w m w w w w w m m m m w w w '
A w m m w ma. mwAAAAmmmmm a . W mA AAWm> a a a a * —A A W " X* Xa a « A AAW m . ^a a * m* a WZ* « %a a a a a a . % ^ m ma . a m. • a ^m m m a a a a X X 3«mmmm a * a X X X mwmmmm a a w mmmmmmmmm a . w mmmmwwmmmm a . a w wm m ^m m m m m a . aw w m m w m m m m m w m m m m ma * a a mw w w w x x a a * a w w m m x w XX a * * a w w m x x * mz*. . * . y a . a a . a
%
—m m m w lim m mm m wa I ilA m m X W II mm a a « a . . . a « a ® ^ a . . . a aw w w A x x w w m m m m m m < w m w z ........................... m a . . . .
__________________ . . . _______________ . . . m w w m x x x x m m m m m m m m w w . * * . * * , * m m . . m x m- V. 9 ® ® ® 9 9 9 ® ® ( 4 9 ® # Z ® ® ® ® 9 9 ® ® ® ® # ® ® 9 ——s ® ® s 3 w w m m m m w w w w w w w w w w w w w w w m m w m w w m m m m m m z x x x w m m ——a —m A w A w ........................ m m m m w w mw w w ® ® ® ® ® ® ® ® w w # ® # ® ® ®u)® ® 9 ® ® w w # # # # w w w w # # w m m x m m m w w w w w w w w w w m m w w w xw w m rn w m m m x m x m m m m A A A w —m m w w w w u ....................... w w mm m m m m mw w w ® ® ® ® * # ® ® w w w w w w w # w # # ® ® ® # # w w w ® # w w w # w w m m m m m m w w w w w w w w w m m w m m m w w m m m m irw m m m m w A m m w —a a w w w w ....................... m x m w m m m m• w w ® # ® ® ®W ' w w m w w w ® ® # # ® ® # ® ® 9 w w w # # wm m m m w w w w w w w w m w* m m m . w w m x w w w w . x w m w w z w m m w A m w m w ....................... w w m m w m m mw w w z ® ® ® ® w w w w w w w w w « ® ® # « ® ® ® ® ® '. z###-m m w m w m W W W W W W W W W W W m m xx AA z x m . • m w m m m w m w * m m m w w w m w • z * m...........................m m m w m m rnm m
——• * w w w ® # ® ® w w w w w w w w w w ® ® ® ® ® ® ® ® ® # w ® w # w w w w w w w w w w w w w w w w w m w m m ___ _ _ _ _ _ _ _ _ wmmmmwm mrnmmmmmww wzzwmwwwmw- * *.-Aa- . awwwwwwwwwwwwwwwww®#®#®®#®#WWWWWWWWWWWWWWWWWWWWW mmmwm wmm wwzwm m.*zwmmzxmw xzzwwwwm . . . a
< mwwwm* WWWWWWWWWWWWWWW®®®#®wwww wwwwwwwwwwwwwwwmmm wwwwwwmmwwwwwwmwxm *> mmiimww zzzwmwmm................. — . ................ 3 9999WWW wwww®®#®ww®# * WWWWWWWWWWWWW' wwwwwwwwmmwwwwm. wwmmwm. wwwwwmuwm ww* * . * *. M . .................. ZZZ9WWW wwwwBsszwwz# * WWWWWWWWWWWWW. wwwwwwwwmmwwwwm* wwmmwm* wwwwwmuwm ww........................
• • ww®®#®B®®ww". wwww. ®#www w wwwwwwww w • wmmww wwwwwwwwwm.www w* mwwwwwwwmmwmwxxw* * • *ww®®»®®®®®®®### mwww®®®wwwwwwwwwwwwww#ww zmmmm m wwwwwwww® mwww * *zwwww * m. . m x* m................w w ® ® ® # # ® # z w w w w w w w w w # ® ® # ® A w w w w w w w w w w w w w w w mmmwwmmm* . m -w m w > w w w* A m w A A . . . w w w m z z w w m m m m m A ,i. . .
m m m ® ® ® ® ® ® ® ® # # w w w w w w w w . # ® ® w w # w w w w w w w - w w w mwm w w . . . . w . * z w w w # u w w m w - * * * mmmmmm w. m zm m * m . . , ® ® ® ® ® ® ® ® ® ® . WWW9WW ® # ® # # w # w w w w w ® —w w w w m m m w w w w » w m . « m. w* w w # # — . w . . * • * z * * * wm mw w w . .®. w®® ® ® ® ® z®®® WWW wwww® w#-wwwwwwww®®w* mwwm. * -. ®---w. z* wwwm > > #- wmm ww mmmmmu uw* u*w®ww®®®®®®®#®®®wwwww®##WWWW' mww® « * ——.......................——w#——_ wm.....................w—w* * « * * xmmwwmmw ww* * * m .
. w w w m w w m m m m
. mmmmrnAmmmm
. r m m m m m m m m • * X m m w m m m
. . . mmmm. . . w w mw m mm m m
. . . . wwmm mm m m
- a — — — — — — m m————— mm—m— — — — — A —
— w m m m m w m— m m m * m m m m — A A — m m m m .*9 3 — — m m m m m m A — A - ^ w w m m m
z u w w ® ® ® ® ® ® ® ® ® rrxw®w®®® ®®®® ®®. .. mwww®® ®»®®®. . . WWW" • * ®®W" W'...mww w®®.....• • mwwww®® ®#®' * ■• WZW ® 9 # ® ® ® ® ® ' '. r* 333393999®®•.•999999#®®®®'. . ® 99 999 9 9 999®'. W 9 # 9 9 9 9 ® 9 9 9 9* ‘. m 9 S 9 ® 9 9 ® ® ® 9 ®. •. I* 99399999®. . . . 9 9 9 9 9 9 9 W W 9 '. . . . 9399999 ##. . . . 9#99 9 9® 9®wwwmmw'. . . z w 9 9 99 9 9 9W W W W # 9 WU- • . .
. . W W ® 99 9® 9 W Z # W W wm ..............
. . W 9 93 9ww9wwwmwwmm. . . .. . . 9 9 3 # 9 9 9 WWWww 9 wwww ..............• • • Z9 9®## WWWWW WWWW WWW. . . .. . . 3#9B®9WWW WWWWWWW...... . . . WW99®WW#9WWWWWW....... . * ZW99 W. WWWWWW*....... . * WWWWWWWWWWWWWWW...................... . . Z W 9 ®wwwwwwwwwwww . W W '*. . . zx 99WWWWWWWWW9W' . W. • *... wrw* WWW WWWWW99WW.............. wwwwwwww* r....... . . . mwwwwwwwwrw m.....• . . rr wwwwrwwwww z ................r..*. wwwwwwwwwwwwr. * r.................• * . wwwwwwwrrwwwr...................... . rrwwwww. rrrw.................. * r. rrwmwwwwr mmm.......... rrz r. rwwwrr. wwm • rrr* > w xrrrr. . . w. r r. wwr rrr r w rrrrrrrrrrwrww rmm w rr r rrrrrrrww w r wwrxixr* zz
rrrr wrrrrwww rwwwwwZZ I rzx
9—#. WWWWWWW' —« * m# . . • ■................ w m w w w w w m w m m m m m................ WWWWWWWWWWW mm m• . . * * w w w w w w w w w w w m m m m m m m . . . . w * -w w w w w w w w m m m m m m m 3 —w D w r w w w w —mm mmm . u m m w w w w w w iw m m m . _ _ _................... w w w w w w w w w w — . m m m m w m m w #w w —WWW. . . . . . w w w w w w w w w m m m m m m m m m ^m w . « w* mm
"O Dwwwww :w m m m m m w w m wwwW'9 « ——— ——«a mm* m mmm w ^ w * *. 9 ———. . w m. m m m z* w m» •
—# —. m mw m m z m . w w jm ' 9 — w w w w w —w wwm m m z • • * • mmm*
mmwiww w*!. m...................m* x* zw mww..................wmwwwwwii. . . . rrw ......... * mwwzzwm’i’i^^A' ................. ww^^i^^^. w# w mmwm . m mmmm . . * z • * ■ mwzmw^wwi "?^w...............* WWW m* mm* zmx • x* • z ■ m* * x- wwwwwwiww' '?'? ............... i ?^ w^ ^• . w ’I'*! • ' * ’iw. * . TH’! w^^w zm w WWW w^www^^^ww wwi. w............ wwmtiwwA wwwwwwwwwwwww ^ ^w................. www m ^%WW1W mmmzwm.............mmnwWiwwwwwwwwwwww www' 'i^^^* z mwwwwwwwwwww www^^^^^n^ a ............ ww^ww^izz * a WWWWWWWWWWW# WW '*I1''I' WWWA...............wwwwmmmw* • m z m* * * w w w w w w n w w w ^ ^ w w w ^ ^ ^ ^ ^ ^ 'iw * • # • • * . w w w w w w ^• * z* . WWWWWWIWWWWIilWWWWW^ WAi,w wwwn^
I* . . . WWWWWW "H "HWWWWWWWilW w w ^ ' l ^ ' ^w w ^ w w w w w w w ^ w n i " ^ w w w w ^ i ^ ^ ^ ^ ^ ^ A A a ........................ w w ^ ^ ^ i ^
m m m w » A w w w w w w w w w m 'T i 'i 'n 'n w w ^ 'n w w ^ ^ 'n 'M ii iA A A A ........................w w ^ i ^ i9 - w w w # - w m w m m . . . . . . . . . . . . . . . . . . . . . . . . . m w w w m m m m w n w w w w w w w r n ' n ’ i T n ' m w A u - i ^ i i - m - n w A A A A . . . . . . . . . . . . . . . . . . . . . . w w ^ ^ ^ ^W W W w - - A # w w m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . w w * m w w A w w ’J w w w w ^ ' n ’ i ’ J ^ T ï ï w n ’ ï ' n n w w n w w ^ ^ ^ w w w * . . . . . . . . . . . . . . . . . . . . . . w w ^ ^ ^ i
. . m m w # * - ■ n w T T H A ‘n w w w w w w T i w > T w w w ^ ‘m ‘* i ' n ' ' i w n ' * i ‘» i M w n w . . . . . . . . . . . . . . . . . . . . . . . w w w ^ ^ ^— — w w w w w i w mw m w w w w w wAl* WW WW#A. a 9 W W ' m W W W * '. w w w m m m m ,* . w w w w w * w m<. m m w w w w w w w w m W W W W W W W " m w w w w w w w w w .WWWWWWWWW# 9.w w w w w w m m W '9 w wW'OWW* .
• w w w w n i 9IM■ WWWWWIMM'■ . . . #—Al®. '
IWW'^'^T'IWWWWWWWWWWW W W W W ^ % " 'l^ 1 ^ ''l ''l 'n ' 'I ^ ^ W W ..................................W 'I'^ '*!..............................w w m w w T i T n w w w w n # w w w n a x x * r o..........WWlIWWWWWIII'nW IWWWWWWWW lllllll' l'nA ww.............. ocooc.......................... w w w w w n w w w w 1 1 1 # WWW#WWWWWW w i i i i i h i i i i w w w a a i i ..........................x o o o o.......................... WWWWWWWWWWW» IW W W A W lW 1 W W W W # W 1 1 1 1 1 1 1 1 1 1 1 1 1 A W A ............................. etC(»0.......................... iw w w w w w w w w w w w iw w w w w w w w w w w w w w i i i m i i m i i ..................................* • 1 WIWWWWWWWWWWWWWWWWW w w l l w . W W # # 1 W W l 1 1 1 1 1 1 1 W l 1 1 a ............................• m iw z m w w w w w w w w w w w # r * w w w w i i w w w w w w w w w w * u u i i i i w w i ..................................o o < » o < «m m m m w w w w w w w w w w w w # w w w i i w w w w w w i i w i * .......................m # # . # a a ...............................o o o om m m . . w* w w w w w w w i iw w w w * * w w w w x m m x ................z * * z u .................c»oooc. . . . z mzxx x x z z z z z xxxzxxxxxx* x* z * * * * * * * z z X Oa a « * a c^oooo
', : i m I #
M I I M I I K O— r P Z i i i i i i i i i i i i S i i i i î ü i i i S i i î i g x l i i i i i i i i i _ w XXX XXX* XIXXXXZXXZXXXXXXXXX XX XXXXIXXXXXO--------------------------- __ XXZXXZX -m w ru r w r r w X X i r r r w X xm _________ ______________________________
IX ■ r r r z x IZ X r r x i Z XXX XI WXXZXXXXXXXXXZXXXXXXXXZXXXr -P ■ • F F r ^ r r ï ï ï ï i i i l ' i S i î l i i i x i i l F ^ i F .
r , . . ^ l i ^ F i x x ? XWW* wr* rw* ww* wwwwwwwww Wr z x r r r r . * . r w . * x r* . x r r x * r r . r . r . * .
. tnBly» [/>— w Bl/îJ : : . . 31
-. * • -~ WW—-. %7" 71 • 77‘7J7171 717771C1 «* ‘ '^'^7171 ^
W— * wm 1 . ...... z. ...37.**. wwmlw— •• 71' • • —. a Bï ... . a .
-WWW— . Ï.'.BIBI. • . : : H .
XX xxxxix . .. I xxxzzxx ..xzxxxzxxx *.• XX X* XZZXZXZXX* .
> w m m w . .
w m :: w m m m — " w w w m m m m -
—. 9W — . :— w m w — w * .
. w m 9 m w B w w • N#— w—WWW* ■
S9®ni9 — 99WW9* B — — f\J99—m w w . — .
B —WIV99W1. 1. . .
. w IWWW 9 "01 "0111.9 9 9 9 9 o n
9999999 J *99999991
-* 9 9 9 9 99 99991
9 9 9 9 9 9 9 9 9 - 9993.99993,3,3 A®
9 9 9 9 9 9 9 9 9 - 9 9 9 9 ® 9 ® 9 -9 ®9 9 9 9 ® 9 9 9 9 9 9 9 9 3 -9 - 9 9 9 3 9 -9 9 -9 X 9 9 9 9 ® 9 9 9 9 9 9 9 -9 9 - 9 9 9 9 9 - 9 9 9 9 X 9 9 9 9 9 9 9 9 9 9 9 9 9 -9 9 9 9 9 -9 -9 9 9 .
9 9 9 9 9 9 ® 9 9 9 9 - 9 9 0 9 ® 9 9 9 .
7171717171 717171 7171
■ * 717171 91X1- * 71717171 .".* ...—- * .* . 71717171717171 . SJÎimSJSTÂ) 71717)71 7171^71717171 7171717)7171 7171— — trtSl
~ 717171
! % pLxI p f ,
. • V>(9* UH/)C/>i
- SS— 99 #99999999399999999399999999-9-99-901- 9** 9 XA® 99999939990 99 99-9999 9 99 999. /->■
m*#— —XA9 9*99 9 99®AAA9®®-99-®9 99A Ori . 3.w KXX 999993 9 9 9 9009® 9 9999 9 9 — AA 1
*4w 9 9— A 9 o 9 9 9 9 B 9 9 9 9 9 9 9 9 ® 99 ®-9-® 9 9 . .m "«m*. w ww.. 99999W* 99 9 9999® 999® 9-99999® O . . . . — J —.
-4 m m**w— ww w 99999 999999999 99®939 99999® w—. . . gz. CCCZCwwH— w 9999999 99® 9 99® 9 99® 999AA® 9-993 . _ . . . . S^ZZZZ
•«'- m 9 9—w 9 9 9w 9999999999*99999999909 OOOOO —. . . ZZ-lZ ww—X—9 999 9 *9->99 9 99999 999® 990.00 OOOOO OO* . . . g
*lw WWW — 99999999 i "i 99 99999 9999990,00 OOOOOO ®,0—. . . .- WWW — w 9w w 9 * ^•>^99999999999 999000,00,"i 99999®. . . , g
• *•-* — w ww — •> -> 1 ">99999999999 9. 00,00 9® 9® 9993. .- - —w — * 9w w 9 * • > 9 9 9 » 9 9 99 9 WW99 99 9 99 9 9 99 9 9 9. . .
ww-wwwww— 9w>*999999999999W 999999999999. * . * CC -f*•*ww_'«»w — 999999*9999999999999999999993393* . . . .
-*. - w ***9999999999999999999999999999999. . . . ^- • W-* *9 9 9 9 *9 9 9 9 » 9 99. 990 9 9 9 9 9 9 9 9 9 9*®®. . . . ? < f _ j _ ,
-*wwww—V9999w9a9*999**9NN->-> ->99999999*3
FIGURE T. FINAL CI CLASSIFICATION MAPSECTION 4
46. . • a x a s •
• • u i i a i M a a a a a a a a a a - a a n s a o a a a a B - • ■aa-»^ - <4 w w >.w k.« .w h.« .> . « • • • t a ia i a a a - a a a a . a a a a n r i n a a a a a a a / y r t a • • j»-u* aaaaaaaBaaartnnnaBaaaarin’ n- . .
w w w w i_ w < .w i.i . t a a a a a a a a a a a a a a r i n n n a a a a a a « * - •* * . .a a a a t M t a a a a a a a a a a r t n n j m / » - » —n* . .
M w w » v .w w . .w « .w > « « * » • * s ü * j > i » f l * o n * v » n - " » - J » n j > i - n j>H te « .» w w w w t e w b > .« n n f n m n n
T f*> n n r» .-> n n n n ** -A j»AS J.V.S.S n n n . i ' i , i n n n . - t " - n s
K w w w w ^ w w A A w A A A A A 3 A A A s n A n , i , i n n ' i n n A n n n n■ w * - ^ w w w A S S A S * A A A * A A A A n n .T . '> n n . 'i , ' i , ' t .^ n n < ‘> . '> n a - . 'i^ w w » . w w A . A A A A A A A A A A A A n i n n n o n n n n n d o n n n - i - «
w A A A A A A A A A A A A A/» A n A ' i n n n n A A n n n n n n » .^ w w w w ^ A A A A A A A A A A A A A A A A ' A A A A A A A A A A A A A * * -
y .^ w A A w w A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A - > - - ‘O S S A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A «•». H '4 A A A A A A A A A A AA A A A A A A A A A A A O A A A A A A X x A A —SNW W 4 A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A Aw S N N A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A « A A A A .............. - t-*
A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A AA><A* • • •ww N A A A A A A A A A A ' A A A A A A A A A A A A A A A A A A A A A A A A AiA A A A..............
"«w AA A A A A A A A A A n n A A C A A A A A A A A A A A A A A A A A A A - A C • • • Cw A A A A A A A A A A A A A A A n n A A A A A A A A A A A A A A A A A A A A A A AAW ' • • i ty w A A -A A A A A A A A A A A A A 'A A A A A A S -A A A A A A A A A A A A A A A A A................i i iS «4 A S S A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A » ^ A " W ' • • • £ • • ww w A A A A A A A 'A A A A A A A A A A A A A A A A A A A A A A A A A A A A A -A -W C X * • • • g ' C f
ww A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A <1 A-* .............. ( i i i iW w w w A A A A A A n n A A A A A A A A A A A A A A A A A A A A A A A A A — C i C C C i irUfVW' « A A A A n n A A A A H A A A A A A A A A A A* A A A A A A A ' • • • ■ < • ................ i * i i i - C• « WWW' i A A* ' • • • • * WW' WWW' f* ' ' U fl ' ' ' ' ' ' ' ' ' ••"■V
• • C
, : : : : 1 Z I l l H U 1 :W (I W 7W tl li "nWlI ’ I ' I I ' ' rW A • il....................................................................7 x ; c ; t w 7 w w 7 w w ;^;K 7 7 ;« w ;x ^ ;< 7 ;*7 W7 7 w 7 7 7 ;*?(;t;< ;<7 7 w ;tw w w ww» ' -nww w w w w w w w w w W ' « >
«•' WWWWWWWWWWW w . « '.......................................................................................................................................... W^»* W W W W W wwwwwww ^ . ......................................................................................................................................................................................................................................................... WA ^WWWWWWWWW^'WW' . •■*1 . . .
.................................................;»wwwwwt.‘** w • ■ • •................................................................ w A iw w w w w st.x,*» w w • awwwwww:*7*.'<.‘*ww a.. . . . . . . . . . ■'■'. . . w w w w ;* x ;* ;* .-* .'« .-< -''« ^ . .. . . . w w w »x ;* ;« .x .x ,-< .x -« -* i .
...........................;* w A w w ;t;* ;* jx ;* ;« ;« X T w ^ ' ; % ? ? ? ? . w w w ? « x x ;^ ;* ;« .x w w ^
................................................. r :^ A ( ;( ^ ;K ;% ;% ? ; (^ ;% ;K ^ ? ? ;^ :% :% ? ? ;K ^ ? ;K ^ ? ; t^ z ;K % ? ? ? ? ? ? ? ; ( ; ( ;K ^ ;K ;x ^ ? x w w A W w ;K ;( w ? ;* ;» w w w ■'•.................................................................... : K x ; t ; ( ? ; tw w w ^ ;x ^ ^ ? ^ ^ ? ;% ? ; ' . x ? ;% z ? ^ ^ :« ;% ;% x :% ? x ^ ? ? ? ; ( ^ ;K ^ ; ( ^ ^ ; ( ; ( ? w w w w ;* w w w % ;» w w w w....................................................................; ( ^ x ; « ^ w w w w w ^ ^ ;% ^ ? 7 % ? ^ ? ? ^ ^ ;% ? ? ? ^ x ;K ;% x ^ ;K :% ? ;* ? ; t ? ^ ^ ^ ; ( ;T x :* ; ( ? w w w w w w ;* ;K ; ( ;< w *....................................................................;ï;*x;«wwwwwuw:*;»; ;* ;<;<;*:*x;«;* ;s ;»;<x;« ;* ;« ;»;* -iw ;*?';«wwww*x;»5»?<;*.-»........................... ....................... w ;( w w w w w w w w :* Al ; ( ^ ; t ^ ; % ^ x ; ( ? ? ? ? ^ ^ ; ( ; t ; ( W W w ; ( ? ; « ? A A w ; ( X ^ ; * ; * ; « ; * ; * w....... W W W W W W W W Z ; * ; * • n^www^^? ». ' » ' ^ . - '
i i w w w w w w w w z ? ^ ? ? ? ; ( ^ ^ ^ ; ( ^ ? ; ( ? x ; * ^ ; ( ; K ^ ^ ; x ^ ? ? ? ^ ^ ^ ? ^ ^ ^ ^ ^ ? ; ( ? w ; ( W W X w ; ( ; * ; * : ^ ; * ; ' . ww?»x a».'*-'';*.xx: . .................; » ; « w w w w w w w u ;* A c ^ ^ ^ ; ' ; '; * ;« ;* ^ x ; ï ^ ; ï ^ ; ^ ;* ; * ;< ^ ^ ^ ^ ^ ^ ^ x ;* ^ ;« ;* ^ ^ ^ ^ ;c ; t ^ A A ; « ^ ;< ; tA » ? t :« 3 » 3 tx . — a .
.................................. : ( ; % w w w w w w w w w w ^ w w ;% z w ^ :% ^ ;* ? 7 ? ? ? ;% :% ;« ^ ; K ? ^ ? ^ ? x ^ x ;K ? ^ ^ ? ? ; ( ; ( ; ( %7 ytytptta:> yt: — ...........................................w w w w w w w w w w w ^ ^ w w ;* w w ^ ^ ^ ;» ; '^ A f ; s ;* ^ : * ^ ^ * ^ ; « ^ ? '? f ? 'x ;K A î ;n ; x ^ ^ ^ A ï ; r 3t A -n ^ ;rw w ? < J« w w w w ■
. w w ^ w w w w w w w : ( ^ w w w w ; t ? x ? ? : % ^ : x ? ^ ? ^ ? ? % ? ^ ? ^ ^ ^ ^ ; ( ; % ^ ; K ? ^ ^ x ; ( ; t w w ^ ,-<;»^»w3« w o •................................................................ w w w x ; t w w w w w X 7 ? ^ ^ ^ ; ( ; % ? ^ ^ ^ ? ; ( ; ( ^ : * ^ ? ? ^ ^ % ^ A ( ? ^ ^ : % y ; t ; ( ; ( ; ( ? ; ( ? x ; ( A w ; * ; ( ; ( :» ;* ;* i;% X T T w •.............................. ... ;* w .'..........................www -■'•.................................................................... . w ? . . x . ... ................................................................. x . x x x ......................................................... ...................................... x x x ; ( x x x x x x x x x x x x x x x x r r x x x x x x x x x x x x x x x x x x x x x x x x . . x x x w ...................................... . . .......................................X X X X W W X X X X X X X X X X X X X X ' X X X X X X X X X X X X X X X X X X X X X X ' . X X X . w .......................... ,
...................X X W W W X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X W X X W XWXWW .................... ... .... . . Il X X W X X X X X X X X X X X X X X X X X ' X X X X X X X X X X X X X X X X X X X X .............. ................ ................................
. . o x x x x x x x x x x x w w r x x x x x x x x x x x x x x x x x x x x x x x x x x x x ' ................ ............................................................... . . . K M X x x x x x x x x r r r r x x x x x x x x x x x x x x x x x x x x x x x x x x x x ..............................................................
x x x x x x x x x r - f i —w r * w x x x x x x x x x x x x x x x x x x x x x x x x x x x x w . . x x . . . . . . . . . .. . . ........................................................... x x x x x x x x w i r r i - r x x x x x x x x x x x x x x x x x x x x x x x x x x x x x . w ' x x x x x w .................................. ...
...........................x x x x x r r r - r r x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x . . x . .............................................
....................... o x x x x r r r r r r x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ................................................... . . ........................................ i x x x x x r r r r - r x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x . x ........................................................................... ...
....................... ....................... x x x x x x x x r w x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x ............................................................................................................................................... O IX X X X X X X W X X X X X X X X X X X X X X X X X X X X X X X X X X X X X x x x x ........................................................................................... .... X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X ...................... .....................................................................
............................................. ... X x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x . w ............................. ......................................................
............... ................... X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X . . ' (/)' w (/> X X ...................................' . . . . . . O X X X X X X X X X X W X X X X X X X X X X X X X X X X X X X X X X W X X . , . » w w w w X X ...............................
. . OW X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X w w XXW X ' X w ' . . <. . . . ................... . ■ . • X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X W X X X X X X X ' w X . . . ,.................................................................... X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X . . . .. .................. . . . . . X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X . . . ................................... ..................................... X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X ' X ' X.......................................................................................... X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X ........................................................................................ |- f -W X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X W X X X w X X X X X X X X . ' ,....................................................................................... X X X X X X X X X X X X X X W X X X X X X rW W X X r-X X X X X X X X X X X X X X X X X .W W X X X X X X X X X X ' . ,w r . r x w x x x x x x x x x x x x . . x x x x x r « x x w x x x . . x x x x x x x x x x x x x x x x x x x x x x ’ i . ,
r r x w x r r r r r x w r r r x x x r r w w r w x x x x x r r r r r r r r r . r x r r r r x w r r r x x x x x x x w x w w w w w x x x x x x x x . ,rr _xw TCC'"^CC_?CCC'"wrCC^(^(^'"^?^CCCCCCCCrCC_ _CCCCCCCjirrrrrrrrrrrr rrrrrrrrwrrrrrrrrrrrrrrrrrrrrri-rrrrrrrm-i rrrrr.-rrrrrrwrwwrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrri rrrrrrrrrrrzr zrrrrrrrrrrrrrrrrrrrwrrrrrrrrrrrrrrrrrrr.
• r r r w r r w w w w i - r r r w w w x x w x x x wwrrrrrr wwwwxxxx wwwww* w w rrrrrwrwi * w w w w w w w w WWWWWWWW wrr. W W W
rrrrrrrrrrrl ........ rrrrrrrrr
w r z z z w r r w w w w r r r r z z w J Z T w r r r x w w r r r r ' - r
i r r r r r r r r r r r r . 2 X 3 T 2 S W w r r w w x r f r r r r r r r r r r r r r nx x x x z r x r r w r r r r r r r r r r r r r r r r r r r r
z w w r r r r r r r x r r x z z z x x x r r r r r r r r r r r r r r r r r r r r *
z r w r r w r r w w r r r z z z z z r r r r r r r r r r r r r r r r r r i - m A w z w w z r z r r r r r r r w z z z z r r r r r r r r r r r r r r r r r r r r i w w w z z w r r r r r r r r z r w z z r n — r r r r r r r r r r r r r r r r r i
i z z z w w r r r r r r w w u z z z z w r r . r r r r r r r r r r r " - r r r r r i
i z r r r r r r r r z z r z r r , - w r x w Z Z Z z r r r r r r z w r r r r r w z x x
z z z z z r w w r r r r r Z r r r z r « r r w z z z z r z w r r r r r z r r r r r r r A z z i z z z r z z r r r r w z w r r r r r x xliiiiPriiiar-ffaüfi^air-Fr r-''
Z Z Z Z r r r u Z Z r r r w A r r r z w x x w x x r u w l j w w r r r r . ~ r r r w . r r r l ' r x x x w r r r r r
I Z r r r r r n - r - r r r z r r r r r r r u r i ^ r r r r r r r r r r r r r r r r r r r r r r r z r r r r r r r w x r r r r r r r - r r r r
r r r r r r r j r r r r r r r r r wr r r Z Z I Z i ' r r ' - , - r r r r r T r r r r r r r r r r r r
. z r r r r r w z z z r r r r r r r - - r r r r r r i - r r r r r r r r r r r r r - r r r r r . - r r i z r r r w z z z u z z r r r i - r r r r r r r n — r r r r r n - r r r ' - r r r r r
Z Z Z Z w w Z r w n r r r n - r r r r r r r r r r r r r r r r r r , - r r r r r r r r r r r r r r r r r r n ~ r.-r-
Z Z Z r r r w w r r r r r r r r r i - i - r r r r r r r r r , - r w r r w r r r r r r r r - Z Z Z Z * r r r r r r r r r r r r r r n - r r r r r r z w w w z w
r Z z r i r r r r r r r r i - r n - r w r r r z r r r r r r r z r w z zw w z w r r w r z w w r r r r r r
- r z i r r r i - z r r r ru m z r r r r r r r r u u r w w r r TJZ w r r r r r r z w w r r r r r r r , * ! -
w i-zzzzzrZ Z w r r r - r | - . - r r w w Z r r r r r r r
u w z z r r - , - - r r r r z r r r r r r r r r r r r r
FIGURE 8. FINAL CI CLASSIFICATION MAPSE C T IO N S
47
Ë- r r r r t - i - n
• r r r r r r r r r r r r r r i ' r r i ' t • r r r r r r r r r r r r r r r r r n • r r r r r r r r r r r r r r r r r n
W M • « «
WWWW« « « « J#WW* • * •
«MMMMMM*^ W •ai» M M M M M «iOa M B* M M crf
MaBMkMMMMMMaBA W« •AWW«
r r r r r r r r r r r r m - i r r r r r r r r r r r r r r r r n i - r n ~ r r r r r r r • - r r r r r n - i
r r r r r r r r r r r r r r r r r r r r r r r r r r r , r r r r i - r r r r r r r r r r r r r r r r r r r r r r r r r r r r r i - r r r r r r r r r r r r r r r r r r r r r i 'i
r r r r r r r r r r r r r r r r r r i j i r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r t tM r r n - r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r
r r r r r r r r r r r ( M r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r
. . . r r r r t j i r r o i r u r r r r r r s v j r s r r r o t r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r i ^ r r r r r r i - r r r r r r i
. . . r r r r r s z z r r r r r r r s z u i ^ z n - r r r r t - r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r
. . . r r r r r r w r w r r r w r mrzzz w r r w u w u r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r n
. . . z r r r r r r r r r r r z z < M Z Z Z t j i r r r : ^ u ê ( M r r r r r r r r i ^ r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r n
. . s r r r r r r r i - r r r i - . z z j z z w w r r w w ^ r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , r r r r r r r r r r r r zz z zz rz r r \ j i r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r n
. z w w r r r r r m m z z z z z z r r r r r r n - r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r n ■ w z r w r r r r r w w r w r z z j f z x r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r n
ZZZZiÀ w r r r r r r unA U ZZ S Z K A r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , - r , - r r r r r w------------------ r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r -------------------------
r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r w w r r r r r r r r r r r r r r r r r r r r r r r r r r r
w r ^ w r r r r r r r r r r r r r r r r r r r r r . zzz z r r r r r r z i j t r r r r n j z ^ T ^ i ) r r r r r , r r r r r r r r r r r r r r r r
. . z z z z z r w w r r r r r z r r r z r w r r r r n - r , - r r , - r r r r r n - r r r r r r r r r
. r w z z z z r z w r r r r r z r r r r r r r w w r r r r r r - r , r r * r r r r r i - i - r , - r r r , - i '• w z z z z z z , - z z r r r r w z w r r r r r ? ; * r r r r r r r r r " , r - " r r r , “ r r r r r r r r r r r r
z z z z r i - - w Z Z r r r w T j r r r z w ? ? w ? ? r r r r r r r r r r r r " r r r r r r r r i - r r r r r r r r r r r - T . - - - - r• w w z iw w " * - i - r r r r r w » r r r r r ? ? ? w r r r r r r r r r r r , - r r r r r r r r r r r r r r r r r r r r r r r r . ----------------. . z z r r r • - r r r r r r Z r r r r r r i ' w r w r r r r r r r r r r r r r r r . - r r r r r r r r r r r r r r r r r r r r - , r r
• • • z z r r r w z i z w z z r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r / ’ r r r r r r ' - r r ,
• • w r r z z z z * r r r r r r r r r r r r r r r r r r r r r r z w w w z w r r r r r r ; r r r r r r r r r r r r r r r r r r .
• • w w z r w r r r r r r , “ r r r r r r r r r r r r r r r r w w z w r r w r z w w , " r r r r r r r r r r r r r r r r r r , - m
. . r z z r r r v r r r r r r r r r r r r w r r z z r r r r r r r r u u . . z z z r r r r r ,- r r r r r r r r r r r r w w r r - o z w r r r r r r z w w r r r ;
■ ' " r r r r r , “ r r ,' r , - r r r r , - r r r - - V - r r r r r r r r r w ■ -
. . r r r r z z r r z r r r z r r r r m w w r w w z r r r r w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , - r r r r r r , - r r
. . zzzzzz r z z z z z z r r u z z z r r r r r r r r r u r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r w , -
. . z z z z r w r z z z z z z z w z z w z z r w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r f - r , - ' - ' - . ' z z z r z z z z u u z z z z z z u z z r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , -
z z z z z z z z z z z z u z z z z rz z z z r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r ,— r r r , * , w z z z z z z z z z z z z i z z w r z z z z w r r r r r r r r r u r r r r r r r r r r r r r r r f - r r r r r r r r r r r r r r r r r r r r r w r r n - <-,
. z z z z z z z z z z z z z r r r z u r z u u r u r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r z r r w r r r r r r , - r r - r r m - w w - o z z z z z z z z z z w w r z z w w w w w o r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , - r r , - r , - ?
• z z w w w z z z z z z z z w z w w ' r r r w w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r ? c . r z z z z z z z r z z z z z z w w w z z r r r r Z w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , - r r r r r , - , - r i
z z z z w z z z z z z w w z z w z w w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , -
w w w w w *w w w w w *,~wwww*
WWi'WW • •
• z z z z w z z z w w z z z z z z w r z z w r i - ............................ z z z z z w w z w r z z z z z z z w w z w r r r r r r r r r r r r r r r r r r. z z z w r r z z z z z z z z w z r z w r . — ----------------------------- -. * w w z w r r r z z z z z z z z z z z z z Zu• r r z w r r r r w z z w z z z z z w z z z w w rrr r r r• r r r r r r r w w w z z z z z z z w w z z w w r r r r r w ; % r r r r r r r r r r r• r r r r r r r z w w z z z z z z z w w z z w u r ' " r ? : r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , - r r r , - r ,• r r r w r z z z w z z z z z z z z z w z z z r r w r , r r r r r r r w w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , - , - , - , - ,• r z w w w z z w z z z z z z z z w w w z z z r r r r r r r r r w w w w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r .• z w z r w z z w w z z z z z z z z w w z z z r w r r r r r r r w w w w w r r w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , - r r r r r r , - i "
* w n r * ww* w z z z z z z z w z z w w z z r r r r r r w w w w w r w w r r r r r w r r r r r r r r r r r r r r r r r r r r r r r r r r r r r , - r r r r . ..................w w z z z w w z z z z w r r z r r w r r r r r r w w w w w w r r r r r r r r r r r r r r . - r r r r r r r r r r r r r r r r r r r r r r r , " , - , -* ■ * « • • w w z w w w w w z z z ; » ; * w w r w r r r r w ^ r u u u r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r u* * * * * w w w w w ;% zzzw zZ w w rrrrr^zw w w ;K * * r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r ? ? w
* w ^w 7?w zw w w w ur* www;?^r*r* « r r r r r r r r r r r r r r r r r r r r ------iT J W w z w w w ^ w w w r r r r ^ r r r r r r r r r r r r r r r r r r r n
m -nwww* • w w r r _ r r r r ^ , - r r r r r r r r r r w r r r r r r r r r r ru^ym?f.
* zrr;t;x??;t.z?rr7( X-,Trrri-r? i%?rrrrrrrrrr '"- "1* rrr rw rr ;* ? * r ;* w rr r r r rw ,
w'n??w w ?* « n w w ? w w w w :*? ? w w ? w w w w ;* w w w* w w w w w ;* w w r 7 jtwnww;*ww???. ?. . ???????rr« * rr-
w w x ^ w r r
—w " - w w w w z w w » • < *« w w w w w z w » - ‘* w
FIGURE 9. FINAL CI CLASSIFICATION MAPSE C T IO N S
00
illI
’ 53, 1 333333333338333333':i i3 3 3 i i3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ii3 . { S W X ? î î ? r i ï . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33-':3333333p3333333333333333-?UîJ?îîîî?îîïîïîîîîîî?îîîîîrîïîîÎ7?ÎÎSÎr!;î
? 0C„ 7 770777» 077777 7 7 7 .7 7 0077 7 74 7 7 T77777T r 777 7 »»_ 7 77» I
M ,. . 3
iii l lÎ1ÎÜÎÎÎÎÎÜÎÎîiiiîîîîü îîîiîiiiîîiliü r»
iiiiiii!!!!!!!iUiU!
# m i i i i k• • î î î î î î î 22i*^0**«45 ^ '^ 54«A7V7. . 455S55555557777777777775555. . . r . . . .
R .
7777777 777 777
7177777 777 777 7 1 1 4 7 7 4 7 4 7 7 7
jv .vinn
...........................................
.............................................. * ............... 4 4 4 4 4 7 ..................5 F 5 3 5 5 1 1 l 1 1 1 1 1 1 1 . 5 5 5 3 5 . T T T T . . 3 0 O O O O O. 1 , 1 : 1 1 1 1 1 1 1 5 5 5 5 5 4 T T T T . 0 ^ ^ O O O T
ono'on
j ü ! i
r 'î î? ,i î
( K F ({ . . . (K X: :: 1
m § > ,( . ti ( ( ( {K
, . ' ! ! ; ? .s ( •
-
':^TtTTrr:?T:1 T T T T T t . . O T . O '- I ' l
l . T T T . T T T . O . . ü ' . i n n V . O T . . . T T T T T T T . Ono'.TOO 'O 'O 'O 'OnO
. 0 O T . . T . . . T T T . 0 0 n 0 0 0 'T .T .T .1 0 * .1 T . O T T . . . . T T . ' . in 'IO M O a O O y n O1 . r 'OOOOOOOOOOO
1 T T '^ O Û Û O O O T T T T . '.lO '.T .lO O O O O O O l . T T T T O O O T T T T . O O O O O O O O OO
l . T T O O O T T . O O O O O O.T T T O O O O O O . . O OO . . O O O 0 0 0 . 0 3 0 O'O
F 4 1 1 1 1 1 H 1 1 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 ................. 5 5 5 5 3 ................................ ........................ ..................... 3 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 r n 5 5 5 5 .................. 3 1 4 1 1 1 1 1 1 1 5 5 5 5 5 4 . 7 T T ..................................................... * H H 5 5 ..................L 3 F F 4 1 1 1 1 1 1 1 5 5 5 5 5 5 T T T .
3 K K ( (
#111
. 4 K K 3 S S ( S S . ( K K K S . {
?l< 51 Issi.?!
Im m llllllll!!!:!!:!#. iijjiliiN îiU x x îH x x îx f::
4 4 4 1 1 1 1 1 1 1 1 1 1 4 4 4 1 4 4 4 4 4 4 4 4 4 1 TH ^ ^ 2 4 4 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 1 ( = 1 1 1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 .H
.‘ 3 4 î i m i l 4 “ 4 4 4 4 4 1 4 4 1 1 1 1 4 4 l ' 4 . * ' h 5 5 S . 4 1 1 1 1 1 1 1 4 1 1 4 4 4 4 4 4 4 4 1 1 1 1 4 4 4 1 . 4 H 5 .
. 4 4 1 1 1 1 1 4 4 1 1 4 4 4 4 4 4 4 P 1 1 1 4 4 4 4 4 4 4 . H H 5 5 . . 4 1 1 1 1 1 1 4 4 4 1 4 4 4 3 f l 4 4 4 1 1 4 4 4 4 4 4 4 4 . H H 5 5
. 4 4 1 1 1 1 1 1 4 4 1 1 4 4 4 4 4 1 1 1 1 4 4 4 4 4 4 1 , H 5 5
S . 4 1 4 4 1 1 1 1 1 1 4 1 4 4 4 4 4 1 1 4 4 4 4 1 3 4 4 . .. 4 4 4 4 . 1 1 1 4 4 4 1 1 1 4 1 1 1 1 4 4 4 3 1 4 . T. F 1 4 4 1 1 1 1 4 4 4 1 1 1 4 4 1 1 4 4 4 4 9 4 4 4 4 4 . T s 5 ..................................................
:l5’:"*3Sîliniiiiilii:. ;§l33;-îiiîii!ll5ii-'ir: m i n M i i i i î m i r ' x
i l î l l l i î l ü î . i l i l i V , J t
* i é ' ‘ ? Î J i i î î î î J i ’ IV r5 5 5 4 1 1 4 1 1 1 1 1 1 1 3 5 5
5 5 1 4 4 4 1 1 1 1 1 1 4 5 M 5 5 55 4 4 4 4 1 1 1 1 1 1 4 5 5 5 5 5 5 E
5 3 4 4 4 1 1 1 1 1 1 1 5 5 5 5 5 5 =5 5 . 4 4 1 1 1 ) 1 1 1 1 1 5 5 5 5 P 5 = :
5 5 P 4 1 1 1 1 1 1 1 1 . 5 5 P P 5 = .
nnno 00 .
• O O O * 'o n .
î o ô ô ' n ' ' iIOOOO n 1000.0 nt O O O O O . . _p OOOO... non! n o o o c ' ! ! . n 1 o n e n n . n 1 c3onnnno. t n o c OOO OO IC O o o o o o o o
O
U .
8
oS
U lce= 3es
w
8 N0I133SdVW NOIiVOUISSVlO 10 1VNU H 3 u n o i d
KKKNfkKKKKKK-KKKKKNKKKKKK
KK>>I>.KKNNNKN • sskkkkkkknk. <h-SKKKKKSh-NS • • •
K K K N K f^ K N K K K » •
K k k k k N k N k k K • • k N K k k k K N N ^ K • • k k k k k k k k k k M • • k k K k k k N K N f > « • • k k k k k k k k S ^ - * • • kkkkkkS SKS * * K k K N K k k K k k K • • kkNNkkKNKN • • • kKNKkkkNK ■ • • • k S K k k k k k k K ) * » • • kkKkkkkKSw • • kkkkkkkkk#<»• kkKkkkkkkk*» • kkkkkkSSSS • • • kkkkkkkkk ♦ • • kkkkkkkkkKk • • kkkKkkKKKN« • • kk f»kkKkkS- • • KKKKK»KKK •kkkkkkkkkk . . .k k N r > K K k k N < • • ' k k k k k k N N K N • • • k k k k k k K N N • • • • k k k k k k N K K • • • • k k ^ K k k k k S • . • • k k k k k k k k k . . . . k k k f . k k k k e » ^ • • • < k K K » > k k k k N • • • kkKKKNNk • . • • k k k k K k k k k K • • • k k k k w k k k k k • ■ • k k k k k k k k k K « • • k k k k K k k k S • • • • < k X k K k k k k • • • • k k N K > » k k k N • • • • k k k k K k k k S • • • •
k k k k k k k k . . . . k k k k k k k k k • . • . k < k k k k k k k k • • • V k k k k k k x • • •
k K k k k k k * " . . . . K N K K K k K k N • • • • < k N f» K k > -* fN • • • • < k k k k k k k < • . . .k k k k k k k k ...............k k k k k k k k . . . . k k ^ K K k k k < . . . . k k k K K k K ^ ^ . . . .k k k k k k k < ...............k k k k K k k k ................
k k k k k k k k ^ . . . kkkkkkkkN . • . kkNKk»» .... kkKKKkk*#""" . • • k k ^ k K k ^ * " " '" . • . kk "kk—«"«- • • • . kffkkkK ......
' r f c r c c r P G C c c c c c ' C G c c G G C c r r c c c r c r c c c c r r c C ' C c r o r c c c c c r o c r c c o c c p o c c r r o G o o c c D o c o o o o o p o c o r • ! T c e c c c : c c T r e c c : c c e c i : m ? ? c r r c : c c £ r c ! r r c ! G c i r c : ! r i . ' ! r r r - r c r r f f C D c : i . * C G r r G G O C i C ! p c c p c c G C i a c G O D r o o c c p c o c c c G G G G G G G G G G G C G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G C G G G G G G G G G G G G G G G G G G G G G G G O G G G G G O G G O G G G G G G G G G G G G G G O G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G O G O G G O G G G G G G G G G GG G G G G G G C G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G C T G G G G G G G G G G G G G G D G G O G G G G G C G G G G G G G • G G G G G G G G G G G G G G G G nG G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G C G G G G G C G G O G C O G D G G G C G G O O O O G G O O G G
G G G G G G G G G O G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G C G G G G G C G C O G G C G O G G G O G O G G O O O G O O O O O G O G G G • •G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G 'G G G G G G G G G G G C G G G O G C G G G G G C G G D G G O G G D G G aO G G G O O G G G G C O G G G G G G C G G G G O G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G C O G G O O G G G G G G aG G G G O C G G C O C C-------------------G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G O G G G O G G G O C C G G G G G G
---------------------------- :---------- IG G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G C _ . i g g g g g g g g g g g g g g g g g g g g g g g g g g g g c g g g g g g g g g g g c c g o o g g g o o o g o g g g g g g g g g g g c -
................G G G G G G G G G G G G G G G G G G G O G G G G G G G G G G G G G O G G G G G G G G G G G G G C G G D G C G G G G G O G G G G G O G G O G G O G G O G G C G G G G C C
................G G G G C G G G G G G G G G O G G G G G G G C G G G G G G G G G G G C G G G G G G G G G G G G G G G G G C G G G G G O G G G P G C G G O G G aG G O D O O G G G G G C
. • . .G G G G C G G G G G G G G G G G G G G G C G G G G G G G G G G G G G G G C G G C G G G G G G G G G G G C G G G G G G G C G G G G C G G G G G G D G G G G G C G G C G C C
................G G G C G G G G G G G G G O O G G O G G G G C G G G G G G G G G G G G G G G G G G G G C G G C G G G G G C G G G G G O G G G G G C G G G O G O G G O G G C G G G rG C
................G G G G C G G G G G G G G G G C G G G G G G G C G G G G C C G C G G G C G G G G C G G C G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G g g g g g g g g g g g c g g g g c g g c g g g g g g g g g g g g g g c g g g g g g g g g g g g g g g g g g c c g g g g g g g g g g o g g g g g g g g c g g g g g g c c GGG GG g g g g g c g g g g g g g g g g g g g g g c g g g g g g g g g g g g g g g g g g c g g g g g g g g c g g g c g g g g c g g g g g c g c g o o o g g g g c g• • • "GG *G • •g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g g c . g g g g g c g c g g g c g g c g g g g c g g g g g g g g g c g g g o o c g g g g g •....................GGG • "G G G G G C G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G 'G G G G G G C G G G G G G G G G G G G G G G G G G G G G G G G O G •>................ GG G G G G G G G G G G G G G G G G G G G G G G G G G G G G C C G G G C G G G G G G G C G G G G G C G G G G G G G G G G G G G G G G G • • • • v v v v v v....................... G G G G G G G G G G G G G G G C G G C G G C G G G G G G G G G G G G G G G G G G G G C G G G G G G GGG G G...........................G G G G G G G G G G G G G C G G G G C G G G G G G O G G G GGG GG G G G G G G G G G G G G G "* v...........................G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G C G G • ' . " " W W W.......................G G G G G G G G G G G G G G G G G G G G G G G G G G G •...........................G G G G G G G G G G G G G G *»"W C................... GGG "k . . W. . . . . . «kk .9k*k9 . ....................ZWZkkkkkk*kkZ**W9#9W W99V99V<99999<C99<9V9W9 V W99WV.......................kkkkkk999kkkk999999999999999999999999999999999999999999999999999999999 999 99999<99 •...............k kkkkkk999»“999999999999.-“99999999999999999999999999999999999999999W99999999999999.......................kkkkkk9k99999999999999999999999999999999999999999 999999999999999999999999999999
»...................kkkkk 9rtZZ99 9k 999kk 9999999 9 9999999999999999999999999999999999999999999999999999999.......................kkkk9kk9^k99kk9(0kkk99999999999999999999999999999999999999999999999999999999999999................... kkk999k9kk999Fl9kkrt»*99999999999999999999999999999999999999999999999«9999 99 9 9 999 9 99.......................k9k999kkkkk999kkkm9Z999999999999999999999999999999 9999999 999999999 99 99 999 9 9 999 9 99.......................... ^99 kkkkk9999kZrtk 999999999999.999999999999999999999999999999999999999999999999................9 ZZ999Zkkkkk9999999 99999999999999999 r99999999999999999999«99999999999999999999999 ............... k CZZkkkkkk 999ffZ99 V 99999999999999999999999999999999999999999999999999999999999^99....................ZZkkkkkkkkk9Z99kZ9999999999999999999999999999999999999999<999999999999999999999999....................ZKSk kKMk999999999999999999999999999999999999999999999999999999999999999999999999................kkkkkkkk9 999k99999999999999999999999999999999999999999999999999999999999999999MM99................kkkkkkkkf) k99999999ZZ»'>999999999999999999999999999999999999999999999999999999999F1«99................9 kkk9f1kkkk999999999kfl99999999999999999999999999999999999999999999999999999................ kkk99kkf)f)99999999 9W999 99 99999999999 999999999999999 9 9999 999 9999999f)99 99 99 9.. . k .9kZ 99kk k 9 99 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 999 9 9 9 9 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 *.9999999 9 MMlOnmg................k Z Z Z Z Z <9 9 i 99 9 9 999 9 9 9 9 9 9 9 9 k k»09 9 9 9 9 99 9 99 99 9 9 9 9 9 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 U ' __................kZ ZZZZ<99Fl999999999999999kk«9999999999999999999999999999999999999999999999 9b.«'l9r>»9................... 9k99kk99Z99999l0999999999^Kk9999999999999999999999999999999999999999999999. . • -kkkkZZkkkVk 9 9 9rtk99 999999 99k9 9 9999 9999 99 9 99999 999 9999 9 999 99 9 ••999 9 9 9 9 9 9 99 999< *'»'999«®__ . . . 'kk kk 9kk 9kkZZM9 9WMk 9 9 99 99 99 9999999999999 9999999 999 9 99 9 9999999999999999999 9 9 • *'*'*9'. . . .kkkkkZ 9k kkk VZ kkZ99919 99 9999 99>9 9 999999999 99 99 999 9 999 9 99 9 9999 99 9 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9)9>ff>ff*r>9t9>r>• . . . Z VkklOv k 9Z k kkk k9999999 9 99 9999 9 999 919999 99999 999 99 99999 9 9999 9 9 9 99 9 9 9 9 9 9 9 9 9 9 9 *»9...................kZZkk99kkkk9999999999999999999kk99999999999999999999999999999999999999999M9*.*.*.*.*" —................... (09ZZ999kkk9999999999999999999999999999999999999999999999999999999999999999999*-»...»-................Zk kKl9999kk999999999V99999999999999999999999999999999999999999999999«999999999999. . . . 'ZZZ9999 '' ‘7 9 « 999999999 9 999999 999 999 999999999 99 99 99999 9 999 9 9 9 9 9 999 9 "9 9 9 9 9 9 9 99 9 9 «.'.90''.'.. . . .kZ99 99 9 9 9kk9 9k9 99 9 9999 9999999999999 99 99 999 99999999999 9 999 99999 999lOnrt9 9 9 99 9 9 9 9 9 ...................9 9K)Z99 k 999999999999999999999999999999999999999999999999V99999 9Mf*9 9999<9999*.999• • . 'kk 9rtkkkk9k 9IT 99 99999kkk999999999 99999999 999 99999 999999 9 9 99 99999 999 9^99 9 999 99 9 9 9 999 9 *.».................? kkkkkkkk 9999999Zkk999999999999999999999999999999999999999999999999999999 99 999^—................... 9kkkkkkKk99999999k9K)9999999 999999999 999999 999999999 9999999 9 99999 99 9 9 99 9 99 9 9 99 9 9 99...............kVkkkkkkkkk9999999999999999999999999999999999999999999999999999999999999999999999V9...............k(0kkkkkkkkkk9999999999999999999999999 999999999999999«999999999 9999 99 9 999 9 99 9 9 999 9 99. • . .kZWkkVkZkkkkkVV 999 99999999999999 999999999999999 99999K>iri9999 999999999 99 99 99 9 99 9 9 999 9 99• • i *k k9K99kkk9kk99 99k99999 9999999 99999999999999999 99999999999 9V9999999 99 9 9999 999 9 999 999 . . . . V9k999in99k99999kkk999999999999999999999999999^nmm9999999999999999999999999999999999................Z9Z999991O 9 9999kZk9999999999999999999999999lO«k«imni09999 9999 99999999 999k 99kkk99999L999...................99K9999 9 9 99 9 9Pl9 99 9 9 99999 9 9 9999 99999 999 9 9*'9199*19999999999 999 9999999999 9k kk k 999f 99*f. . . k kkk99999k 9999999 999999999999999999999999999999999999999 999 99 999 999 999>l09kkk 9 999»>99• . . .kkkkkkk9 99999999999999999999999999999999999999999999999999999999999999kk99999999999 . . . 'kkkkKkkkk9Z9kk999999999999999999999999999999999999999999999999999999999kkk9 Mk 999 9 99 . • «k kkkkvkkkkkpik 999999999999999999999999999999999V9* 99999999999999999999TmP Mmk k999999. • . .kkkk99k9kk999999999999999999999999999999999999999«'9999999999999999f099999l^’«19k9'9k99999• • . . k99999999999999999999999999999999999999999999999999999999999999K)^9999 9999 99 99 999 9 99• .. k99999999999999999999999999999999999999999999999999999999999999kk999999999999999999• . .9 .k9MM9999k999999999999999999999999999999999999999999999999999999ll099999 999999 999 k9Mk.• • •9ZZ9kZ99999999999999999999999999999999999999999999999999999999999999 99 9999 9999^«9«W• . . Z9k9999999999999999999999999V99999999999999999999999999999999999999k9999Uk999lOK>l9r>k9t...............k99999999999999999999999999999999999999999999999999999999999999999 9kkk9999kVkkkkkkM. . . . .2992 9109999999999k999999999999999999999999999999999999999999999k99kkkk 9999kk kkkkk• • ‘k ■ 9k9 k 999999999999999999999999999999999999 99999999999999 999 • 9rtkVkkkkk9999kkkkkk •• • kk *kZ99k9kk99k99999999999999999999999999999**9V999999999999999999kk99 kk9>k VMkkkkkkK-J' . "kZ k k k k lO k k 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 k k k 9 9 9 9 9 lO IO rtkk kk •'’k k I X I. . • . kkkk99k99k9999999999999999999999 9999999999999999999999999999999999999k9kkkkkMMkP’H. « . .kkkklflkkk999999 9999999999999999999999999999999999999999999999999999k99kkkkkkkkkP’f’MMXI. . . . kkkkkk9999999999 999999999 99K)999999999 9 99999999 k999999999999999kkkkkkkkkkkkkMMflM X ‘. ■ . . kkkkkkV99999999999999999999 *-99999 99999999999kkk9k99999999999kkkkk 99kkkkkkkkk^l'’ f’l ". • . .k9kkkkk9k f99999999 999999999 **99999999 99 9999M9 9 9 999 9 99 9 99 9 9 9kkkMk9 ..................*
kkkkkZk9999999999kk9999 •9999**99 99 99 9 • * 9*- **** . . .H- .*• . >**9lO
I
k 9 k k 9 9 9 k 9 9 k 9 9 9 * * * “****** •
Ul CflOUltO .
. tOtOUl . .UltOCOUlUllO tOtOUl (Oÿul
. . . tOUlMUl ........ uiirt• • . (/I GUlUl • Ü1. . » i/iuiulco "O. • • ifimi/) Cl• . — j/)Otncii/iioci.1 . . WlOClc/llO .. . . .11 c ic ii /id .(/)• • . •t'» ClOOClCl Cl
................... Cl Cl Cl Cl
ooor o rx j •. . . .oooi>r xo • • CXOOI o o x x
■kHkK*"** . . . .(/ICICl . *C1 «C1C1 .[1 . . .•5 .t£ . . . "U; . .Cl Cl Cl «clOCl . .Cl
. . ü f ....................... . IXIX . ■ CIOCIOO Cl Cl cl c l c l . . . c l c l c l . . . .3 i ï i r i r . • Cl . c ic ic io c ic ic ic ic i c ic i c ic i c i » .c 'c ic io c ic , o c i • . .c i
i r • oC l CIO c ic ic ic io c i c ic io c ic io c i . c i c i o o c i c i o . . . . . .00Cl • o c io c io c io c j c i c io CIO O O O O O O O O .00 . . o 00000 .000 00 00 • .00 o o o o o o o o o o o o o o .0000 "OOO .0000 o "OO O O O O O O O O .................... o o o o o o o o o o o o o o o o o o o «0 .0000 .0O O O clO O O . . 000 O O O O O O O O * "OO O O O tlO O O O O O O O clC lO O O O . . 'O O O ' . 'O O O O O O O O . . . . O O O O O O . o o o o o o o o o o o o o o o o o o o o o o . "OOO . •
I 0000 000 ........................O O O O O O O O o o o o o o o o o o o o o o o o O O O O O O O O O O. .0000 . 00 . . .0 . . "O OOOOOOOO .O O O O O O O O O O O O O O O "OO O O O O O
O "OOOOO O O O O O O . —O O O O O O O O O . "OOOOOOO. 1000000 . o o o o o o o O O O O O O O O O . O O O O O O . • "O O O O O C .O O oO O O O O O O O O O O O
00 . "O 000 "OO . ^ ^^000000 00 .0000000000000000 . . . . . . .O ................... o o o o o o o . O O O O O O O O O O O O O O O O O O O O O O O O ...........................00 . . . . O O O O O O O O O O O O O O O O O o o o o o o o o o o o o o o o o ..............................
00 O O O O O O O O O O O O O O O o o o o o o o . .00 00 .......................................................... ^ O O O O O O O O *00 . ...........................
"O . o • . "O . "O OOOOOOO . "O . . . "OOOO "O ......................................................00 .c l .0 ...........................o . . " o o o o o o o c . ' "OOOO 00 0 c l c . . . . . . . . . . . . . .........000 000000000000 . . "O CO..................
I .00 . . . O O O O clO O O O O clO O O . . "O " I t "C l.............................................................00 000 . . "O "OOOOO OOO 00 ................
O 1; ................O O O O O .O O O O O "O «OOO OOOO O
000 tr O O O O O O O O 000 .k' . O O O O O 00 . . • .
i r k k O O O O 00 ................
OOO O "O "
O O O O . . . •O O O O O .
•X 'O O O O O O O • O O O OOO
. O O O O O • •"OOOO . o
o o 00 o •................ ..................................................... O O O O O O O O O . .
. . . . . . . . J . . - I X . • . " I o o o o o o o o o o o . ........................... i r x o o • . "O OOOOOOOO 00 • . ....................... x x x x o o o o o o o o o o o o o o • 00 . ........................... X X X O O O O O O O O O O O O O O O I'O "OOO . ■' "XX . . . . X X X X X l'X X O O O O O O O O O O O I' 000 . .
.......................o o r x o o x i II " O O O O O 00 000 n 00 • • •................X 000 X X IX O O O O O X O O X k k k k ................
. . . .K . . . . . . "tJ Ii .klCI*-***” .. .... . 'C- . "klklU • *.*-■-.*• .— : kl kl • • "kul ""***. . G G • "W
. . . «WWW""W-*^U 'GC'** . . .: t ’kJ"*“. ^ u — . Il . G . . .
i . «G G . . — . .«GG G . . .... .H "U:
. "GG "G . . "GGG . "G *
. G G G G G G G G G G GC
. "GG . "GGG . . "GC
. . . -CCC- . . "GGGC"k . . . . -G G C CGG G G G . > 61GGG
6 ÿ
o
a E f c .. 1
4 .T T .
: t t Tt .
-T .
BSâSâ‘-“§§i88---''§8i88ùââ 388888888888S8§§88“ 8888888a'□QQQOQQQOODDOOQOOâ OOOOOOOO^
sggg§§§§§g§§§§§§§§°Q Q O O Q Q Q O Q Q Q Q Q Q O Q O O O O Q Q O Q Q Q Q Q Ô
8§g88S8888§gg88e8§888g88gege§?Q o a a a Q O Q O O Q a a o a Q Q a o Q Q Q a a Q O Q Q a BOOOOOQOOQOQQaQQOOOOOQQOQQQaQQ OOOOOOOQDOQQQQQaQQOOQQnQOQOOa QQQOQQOOOOQQOaQQaaOQOQQQQQQOO QaOOOOQOOOOOOOOQOQOnOOOOOOQQOB§§s§§8§§8§i§pOQOOOOOOQQQaOOOQOOOOQQQQQQOOÔ BBB UOQQOOQOOQOOOQOODOQQOOOOOOOQOOBBBt □□□□OQOOOOQOQQOQOOOOOQOOOOOQOaeBB OOOQQOOOQQOOOOOQOOQOQOOOOOQQOOBBBB QQOQOOOOQOOOQQQQQQQOQOOOOOQOOOBBB OOOQQQQQOOQOOOQOOOQQQQOOQOQDQOBBBOOQQQQQQQOOOOOOOQQQOOOODOOOOOOBBB . ________S5SS999S9S99009009990099a99890BBBBBBBBBBBBe
• t :
7 /7 7 7 ? . 77 77
ViUUUr
0 OO DOOODDDDCDCOC A Ob OO. O07DODOOODODOOOOOODDnn OOOOOOOO 0 ODDOODODDOOODDCDDOOOOOOOOOOOOOOOOOO DDDDDOOrùDDDOOOOOOOOOOOO.000 70000000
DODODODDDDDODDDDODOOOOOOOOOOO. 700D U 00..9 0
8888888o8888888gBBBSBBB_MBB_goSSS 88888888888888'"
- B B B B B . . B S B E B B B B B B E B B BOOODDDOOOOODOOODOODODDOOODOOOOO. .OOOOOOOOO .1 . .7DOOODDODDDODDODDODDOODOOOOOOOO . DDOOODDDDOOC
77 . 700DOODDDOOODDOODODDOODOOOOOOOO? OOOOOOOOOOOOO _____________7777 7DDDDDODDDDOODDODDOD 0 0 OOOO OD70DODDDDODDODDDODDODODODDODODDODDD.7 7 77 700 7700 7070 O . . 77777 O ---------------------------------------------------------I I ’.666'. X I X ' q q I I X . . . . Ô Q Ô ô ' v v i ' v i lOQOQOaOQOOOOOOOOOOOOQOOQOOn'1'-)''JO .
8888888°
88888XàoOQOOQQ* àOQOQQOQOOOQOOQQOOOOOOOQOOOQOOOOO'-TT.in . . . aQQQaQOQOQOQQQOQQQQQOQQQQOOQQaQOQOOOQQOQQOOnnon. .
:iaHiRiaaRsiiiRiRssi3i3HS3ai33aaRaasls;issasssî§5655565556BB^B E E E .
, OQQQQQOQQQQaOQQaaQQQQQQQOOQOOOQOQOQOOaQQOQaOOnonOOOOOnCJO. . 77 _ ____________________!l§88888gg8§m§§§gg§§ggg§§§§§§§§§§§§8a88888388888888888 *in!!ggg§Bggggggggggggggggggissm sm aagas.??::.
.1
.888888888888888?:::.OQQQQQOOQQQQQOQB. . . . 000000000000000.. OOOOOOOOOOOOOOOO
. OOQMOOQOOOOOOOOB , 000000000000000
. OQOQQOOOOQOOOOOB
"i ggggggggggggggB
. , . . 1 lOaOQQUOOOOOOOOOOOOl
B . 6BBBBBBBB = ë '"g g gBBBBBBBB.=gggggggg°IBBBBBBBBD
BIBBBBBBBB
AOOOQQOOOOOOOOOOOOO 71%. AOOOODOOOOOOOQOOOOO 7771
. . . .OOOOOOOOOOOOOOOOO..1711 . . B i t BOOOQOOOOOOOOOOOOOO . . 1 .BBB BBBOOOOOOOOOOOOOOOOO.1 . t B B ! .BQOOOOOOOOOQOOOOOOOl T T l l . IB S iBQO OO O ooooonnnoooooi * BBBBBBOOOOOQQOOOOQOOOOOO '
.BBBBBBOOOOOOOOOOOOOOOOOO , , BBBBBBOQOOOOOQOOOOOOOOOOl.%
,7 7 7
t h ;
l % 1 . I • I I » !
T ? T t : : : + 1 ; :. ____________________ __ IBBBBBBBBBBBBBBBBBBOQOOOOOOQOOOOOOOOO. . .OOOOOOOOOOOOOOO BBB8BBBBBBBBBBBBBB8BB.OOOOOOOOOOOOOOOOOO T T . . .OQQOOOOOOOODOOOOB8B88BBBBBBBB8BBB3BBB OOOOOOOOOOOOOOOOO.1 . , .. . .QOOOOOOQOQOQOQOOBBBBBBBBBBBBBBBBXHBBB OOOOOOOOOOOOOOOO. . . ,T . .T . . .OOOOOOOOOOOOOOOO BBBBBBBBBBB B I I I I BB OOOOOOOOOOOOOOOOO. , T.: ::88SSSSSSSS888SS8iiiiliiiiiiiâ. " !’i .11188888888888888888: : ; TU. . .QOOQOQQOOOOQQOQQBBBBBBBBBBBBBBBBBBI1 IB B . OOOOOOOOOOOOOOOO. . T1 T _ I . . ._QgoggggggogQOOOBBBBBBBBB8B8BB BBBlIIBBOOOOUOOCOOQOQQQQOO 1 ,1: : : 0aaa0000a0008888BBBBBBBB88BBBBBBBBBBBBB88888888888888888' ■ • • S 3 9 9 3 9 S S S S S S S S S 9 l g S E S S S S S S B g ' ? E g a S S B B E . : 9 S 9 9 S S E 9 S 9 9 9 9 9 9 5 5 - ï I > > t U i . ? ? ! t
T Î U t l ’' : l i t : ?T » , 1 1 , i , J t
.GGmgggggggmgBB:..r{|tît..888888°°°88B§8°°°• • Ï t Î Î • • • • • • • • . . . D D o
H
i l
T , , T . T T
. i .
T Boa: : :Î t 8 8 8 ” ° - ° 8 8 o"
T Y T T . O O O O O. T T . . O O O û O
.0
BBBBBBBB#
000000000000000000000000000000081 DQOOOOOOOOOOOOOOOOOOOOQOOOOOOOOBbaig o o g o o o o o o o o o o o o Q Q o o o o o o o o o o o o o B Bl
8888888888888888888888888888888 : .1100000000000000000000000000000001' OQOOOQOOQDQOOOOOOOOOOQOOQOOOOOOQB 0 0 0 0 0 0 000 000000 00000 000000 000000 8 . OOOOOOOOOOOOQOOOOOOOQQQOOOOOOOOOBBI OOOOOOOOOOOQOOOOQOOQOOOOOOOOOOOOBBboo . OOOOOOOOOOOOOOOOOOOOOOOOOQQOOOOOBBBBBB. OOOaOOQQOOOOOOQOOOOODOOOOQOQQOQDBBBBBB .g g o g g o o g g g o o o g o o o o o o o o o Q o o o o o o o o B B B B B B B .000000000000000000000000000000000060800000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 800000000000000000000000000000000000000000008 OOOOQOOOOOOOOOOOOOOOOQDDOOOOOOOO BBBBBBBBBBBB
E E E E E s E E ll i i iE l l i i l i i i l i i . m:888888888888888888888888888888888=111111111111 88888888888888888888888888888888811111111111111 s.OQOOOOOOOQOOOOQOaOOOOOOOOOOQOOOODBBBBBBBBBBBBBB0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 ------------------------OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOB
OOQQOQOQOQOOOOOBBBBBBBBBOBBBBBBBB ----------------------- OOOOQDOOOOOOOOOBBBB IBBBBBBBBBB _ ____________________
i i i i i i i i i i i i i l l l *I l . îîl ? X .
11
b b b b b b . . g g g g g g g g g g g g g g g g g B BBBB . . o o o o o o o o o o o o .
OOOOOQOOOQOQOOOOOOOOOQQQQOOOOQOQOBB
wwwOOÔÔOQOOOOOOQ
■88888888888S88S88iiiiiiiiiiiiiiiiiiiiiiilssi°s” °°“°°°° BBB;:D888883888S8888881111illiillBlillillliBB:SSSS
:S8S8S88S888SSSSS8111........................... .........IoOOOOOOOOÜOOOOOa^?^0BBBB%BBBBBBBB8QBBBBBBOOnÔoàoÔÔÔÔâÔÔâ'
. . . . . . . t i i i l i l l S
f x î ï 1 l l i lI I I I I Y T T T T T T T T T T
Tî” "
1 :1 1 1 .1 .1
iB B B iB B B g g g g g g g g g g g g
000 000000 000000 00000 000000 000000 0 BBBBBBBBBBBBBBB 0000000000QQ000000Q000000000000000BBBBBBBBB6BBBBB 0000000000000000000000000000000000BB8888BBB8BBBBB OOaQOOOOQOOOOQOOOOOOODOOaOQOQQQOOQBBBBBBBBBBBBBBB OOQQOOQOOOOQOOOOOOOOQQQOQQOOOQQQQOBBBBBBBBBBBBBBB OOOOOOOOOOQODOOOOOOQOOOOOOOOOOOOOOBBBBBBBBBBBBBBBoao oaoooQ oaa r--------------------------------------------- -------- ----------------------OOOOOOOOOOOO!
. OOOOOOOOOOOOOOOOOOBBBaBBBBBBBBBBBBB .
. OOOOOOOOOOOOOOOOOOBBB>3BBBBBBBB BBBBB;8 8 8 8 8 8 8 8 3 8 8 3 8 8 8 8 S 8 B ! i'T g i? ! l!B , .1 1 ?
BBBBBBBBBBBBBBB IBBBB OOOOOOOOOOOOOOO!* BBBBOOOOOOOOOOOOOO01 1 1
BCBBOOOOOOQOOOOOQOO 1 " T 1 ! . .OOOOOOOOOOOOOOO 1111
IBOOOOQOOOOOOOOOO 11111111 . . B . OOOOOOOOOOOOOOO 11111OOOOOOOOOOOOOOOOO. ooo o o o o o o o o o o o o o o o o OO. . . oooooooOOOOOOooooooooooooooOOOOO
. . ooo ooooo o o o o o o o o o o o o o o o o o o OOOOOOOOOOOOoooooooooooooOOOOO . . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ooooooooamammggmooooooooooooooo -------------- ^^^^“pOOOOOOOOOOOOOOtlIlOOObOOOODDODOOOOOOnOOOüOOOOOOOOOOOo|1j1111.11'
1 1 1111 i 11 i T .ir. T
'l î îîî
i ïuo
i l l i
imei
51
« • n H H « « « »• • • « « HH* HHH H* HI• HH* H* • O* HHHHHHHH* * « * * HHH*4H'-WH * • C/ HHH* C* O
- * HHH*4« H6000HHH* HHHHHHH* HHH
HHHHHH HHH
Cl. • C C C i^
iDoao^ef^
Cm • • • O O O J O OOO O............ O O O O O O
* • * O O O O O O O * O O O O
O O O O O O OO O O O O O a oOOOOO’ « *
• O O O O O O
p o o o o c x 3 o i x y r o o o c x x j
> -(.4HHH* . • » * • * H* 'MftJ. . . ..m m m * m m m m m ;. &
* 6 w w m m m m m m m w i i mmmmmmmm m* m m m m m x mwm wm i i x i m m mmmmmmm m
mmmmmw'? mmmmmmwm x x » w m m m m m m m m m m m m m *A A w m m m m m m m m m m m m m i* * x i * j * m m m m m m m m m m * * * ^ * * ^ m
mmmmmmmmmmmmm w m x x x x m m m m m m &** mmAAmm* ?*mm m mm m m m m m m m m m wi x x x x * rm m m m m u^A m m m m m m m m m m m m m m m m w m m m m m m m m w iii x * • i * * mmm* mm* * * mmmmmmmmmmmmmmmmmm x x x x x x x x * * * * x *mmmmmmmmmmmmmmmmmm m i i x x i i x x i i i x x rnm mm m mm mmmmmmmmmmmmmmmmmmwmmwxmm w m x i i x * * * m mmmmmmmmmm m mm m mm mm m mm m mm m mm m mm wmm ^m m m*• _ _
xm m m m m m * «mmmwmmmmmmmmmmmmmmmmmmmmmmmmmm** a o o?(ww mmj*m;«. * * wmwm mmmmmmmmmmmmmmmmmmm mwwm uxx mww* 5»mmmmmmmmmmmmmmmmm n -i *mmiw X 3»w w?«3*»mixx xi;** mmmmmmmmmmmmmmmm* m* * m%?x 3»xw3'?t:» 7t . r:*w;<mmm. mmmmm* i* zmm *wwxix x mix * * xx* ixx* * ............. w* * mm.
• H O HH O * * _____________H . ..............................HOH H* O* O O O O H .
OOO* O * * * H H O ...........................* « H* .** * « H« . O OO OO** * * O O O O O O O H* H H H H H* * H H .................................. O O O O O O O O O O O o* *
o* O O O O H h o o * * * * H H« ' * . * ............... o O O O oooooooooooooo *O O H H OO* O h H * H OO* * * H H > ........................ O ooooooooooooooooooooooooooooH . * H H H * H* * O* O H * . * O O O O O O O O ooooooo* ooooooooooooooooooooo*
* . CtJCOOOOO O OO ooooooooooooooooooooooooooooooooooooooo ** oooooooooooo ooaoaaoaaaaaooaaooaaaoooaaaa ooooooo O OO OOOO O D O oooooooooooooooooooooo O O O O O O O O O O O O O O O '<*OOO O O O O O ooooooooooooooooooooooooooooooooooooooOOO O * o * * oooooooooooooooooooooooooooooooooooo
OOO OOOO OO CO 0000000000000000000000000000300000000 OOOOOOOOOOOOC9 ooooooooooooooooooooooooooooooooooo*
OOO** O O O O O OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO O'OOOO* O a OOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO*
OOOO OOOO coo 000000000000000003000000000000000* SOOOO OOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO N
ooooooo O O O O O O O O oooooouooooooooooooooooooooooooooo OOO OOOO ooooooo ooooooooooooooooooooooooooooooooooo * OO aaa oooooo ooooooooooooooooooooooooooooooooooo
* O O O O O o oooooooooooooooooooooooooooooooooooOOO OO 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * *
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO * H OOO OOO 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 *
OOO 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 * *
...........................................* * • Ttmmmmmmmmmmmmmm m* * o
............................................ w x x ^ ^ ? ^ : « mmmmmmmmmmm wm* *
. . . ytjCé . w* u x x i x i ^ t u x w i 7«mmmmmmmmmmmm * * * *Ttmwuwmmmw xw w w w w x?w m mmmmmmm^mmmmmmw m *
jimm mmmmmmm* wmmwwwwmm?%wwmmmmmmmmmmmmm * a mmmmmmmmmmmm mmmmmmmmmwwmmmmmmmmmmmmmmm* * * mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm m* * • mmmmmmmmmmmmmmmmmmm immmmmmmmmmmmmmmmmmm mmmmmmmmmmmmmmmmmmm-. immmmmmmmw&mmmmmmmmm* mmmmmmmmmmmmmmmmmmmrnmmmmmmmmm»mmmmmmmmmm mmmmwwmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm*m** oo mmmmwmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm ■ mmmmmmmmrnmmmmmmmmmmmmmm mmmmmmmmmmmmmmmmm*II mmmm mm m% mmmmmmmmmmmmmm mmmmm mmmmmmmmmmmm* mmmmmmm mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm* • mmmmmmmmmmmmmmm;» mmmmmmmmmmmmmmmmmmmmmmmmw mmmmm mmmmm mmmmmmm mmmmmmm mm mmmmmmmmmmmmm II i mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm* i mmm mmm mmmm mmm mmmm mmm mmmmmmm mmm mmmmmmmmmm;; . . . mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmrnmmmmmm m* * mmmmmmmmmmmmm- immmmmmmmmmmmmmmmmmmmmmmww*w* *mmmmmmmmmmmmm-*: I ^mmmmmmmmmmmmmmmmmmmmmm..................mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm m** • . .
Igmmmmmmmmmmmmmmmmmmmmmmmrnmmmmmmmmmmmmmm m*. . |mmmmmmmmmmmmmmmmmmmmmmmmmmmmmm*mmmmmmmm6w. .
rnmmmmmmmmmmmmmmmmmmmmmmmmmmmAAm***■mmmmm mmmmmmmmmmmmmmmmmm mm mmmmmm-imAAm**.Nmmmmmwmmmmmmmmmmmmmmmmmmmmmmmmmmmmm *m *w * Bmmmmmmmmmmmmmmmmmummmmmmmmmmmmmmmmm*rn**A* mmmmmmm mm mmm mmmmmwww mmmm mmmmm mmmmm******
mmmmmmmmmm mmmmmmmm wmmm*mmmmmmmmmm***** * * * * * mmmmmmmmmmmmmmmmmmwwmmmmmmmmmmmmmm****w***A* mmmmmmmmmmmmmmmmmm mmmmmmmmmmmmmmmmmmm****** mmmw xmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm*****, mmm w mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm***** mmmwwwmmmmmmmmmmm mmmmmmmmmmmmmmmmmmmmm*****- mmmmwmmmmmmmmmwmmmmmmmmmmmmmmmmmmmmmmm***' ii. • mmmmmmmmmmmmm**wmmmmmmm. • mmmw. xx» o o o o o o ii mmmmmmwm mmmm* * * * w • x iic»oocioc»c> o o o o o o o o o o oUWWWWWXXX ' OOOOOOOOOOOOOOOCIOOOOOOOOOCIOOOOO'OOOOOOOO o o o o o o o o o o o o o o o o o o c io o o o OOO o o o o o o o o o o o o , O O O O O O O O o o o o o o O O O O o o o o o o o o o o o o o O O O o o o o o o o o o o o o o o o o o o o o o o o o o o o O O O O O O O O o o o o o o o o o o o o o o o o o o o o o o o o o ooooooooooooooOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOo o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o oooooooooooooooooooO O O O O O O O O O O O O O O O O O O O O O O O O O " o o o o o o o o o o o o o o o o o o o o o o o O O O O OOOOOOOOOOOOOOOOO oooooooooooooO O O O O O O O O O O O O O O o o o o o o o o o o o o o oooooooooooO O O O O O O O O O O O O O O O O O o o o o o o o o o o o o o o o o o o o o o o OOOOOOOOOOOOOOOOO* ■ OOOOOOOO o OOOOOOOO. OOOOOOOOOOO OOOOOOOOOOOOOOOOOO o o OOOOOOOO • OOOOOO. . o o o o o o o o o o o o o o o o o o o OOOOO o o o o o o o o o o o o o o o o . . x o o o o o o o o o o o o o o o o o o o o o o o o o x o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o -OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO-O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o -POOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . . POOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.o o o o o o o o o n o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o I o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o OOOOOOOO o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . o o o o o o o x o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . o o o o o o o O O O O O O O O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o .OOOOoOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o .o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o .o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o *o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o oo o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o n o o o o o *
OOOOOOOOOOO. o o o o o o o o o o o o o o o o o o o o o o o o o o -O O O O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . . .
o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o * o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O O O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . . o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o -OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOllo o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o oOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO O' OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO O' ' OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO. O' , 'o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . . <OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO. . < OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOIIII- OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO II- OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOll II'o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o . > • ' o o o o o o o o o o o o o o o o o o o o o o o o OOOOOOOO OOOOOOOO OOO. OIX-
. . X* r m OOO oooooooooooooooooooooooooooooooooooooooo.o ooo« N ..X ... X« wmw 30 330000000030000300000033000000330030000000 03.. 77 . . 7 77. . . 30 3000000300000000330300000000300000000000000 OOOO'7 . mmw7 7 O 0030300033330033003000000300000000030003003033000. .
7 7 m m m m . . m* • . . oo oooooooooooooooooooooooooooooooooooooooooooooooo . mmmmmmm w - oooo ooooooooooooooooooooooooooooooooooooooooooooooo .0000303003000000000003303030000300000330030030.
00003000000000003000003000000000003030300003330' 0000000300300000303000300303030000000300000'300' 003033000030300330300030000300333330303300. . 33<000030000030000000000030000300300000003000 ..OOO 00000300003300030000003300030000303300000000 OOO 00000330000030000000000300003000000003000000 OOO* 'lOOOOOOOOOOODOOOOOOOO.rOOOOOOOOOOOOOOOOOOOOO* 003. 030003000030000000000033000300003030000000" • • 03. 000003000000030330000033030000000000000000.* 30.OOOOOOOOOOOOOOODOOOOOOOOOOOGOOOOOOOOOOOOOOO. • 30 . 000000000000000000000000300030000300000000 C O. 30 .. 00000000000000000000000000030000000000000 . 19 oo* 0000030000033000000300003300300033300000000.O O O O O 000003030000000000300003000300003000300000. (9 30-
000000303000000030000000300030000000000000.. O- 00000030000030000300 003300030000000000000 • OOO* ■ 00000300000000 ooooooooooooooooooooooooo . O O O ,
OOOO ooooooo 30300000000300330000000.O O "• i OOO OOOO aa ooooooooooooooooooooo . o . . . . oiO 30 ooooooooooooooooooo oooooooooo O O O -.. I3 03 ooooooooooooooooooo 300300000000 O»-. O -oo oooooooooooooooo 003000300000000000 o 30 oooooooooooo . . • ooooooooooooooooooo
300 333003030033 30330300030 330333333 33'OOOOOOOOOOOOOOO .. OOOOOOOO . o o o o o o o .O'O*'OOOOOOOOOOOOOOO • • OOOOOOOO . ooooooo. o. o.o ooooooo oooooo. . • . ooooooo oooooo . 00 .3 OOOOO 00 O' ... • oooooo 30 OOOOO* . * OOO.OOOOOO" . oo OOO O OOOOO" OOOOO" o ................OOOO" . 0 OOOOO ...... 00" ....... — a. hh. *
H. . L9 3 03 3" . . HHH HH. . O 333333 . . . HH . HHH • 33333033 . . . n n hHHH. 0300000019319 3. hmHHHHH . 19 3003303. I9i9. . . hHHHHHH . . 3 00303 . . . . .MW.HHHH. . C9000000 . . . hh.mhhHhH. . 3303000 . . HHH.«k,H. . 3 333330 19.' . 3 3 3 3 3 O" . HHH.MM.MM.M. « 3 3 3 3 3 3 3 " .. 3 3 3 3 3 3 3 O O O " . h h h m »m .m m h' 3 3 3 3 3 3 O O ' .
FIGURE 13. FINAL Cl CLASSIFICATION MAPSECTION 1 0
CMm
Ml . " î i i l l , : ï l l l l l l M » ...................................... . 777777777• • • • • • • • • • * # . . . . . . . . 7 7 7 7 7 7 7 7 7
o o o o o o o BOOOOO OQQQOOQQOOOOOQOQOQ OOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOO 0 0 o o OOOOO OOOO 0 oO OBOO OOOO. O.............ow oo
o o . OOOOoooooo o oo OOOOOOOOO 00 o 00 o o o o o o o o o o o oOOOOOOOOO O O OOOOOOOOOQQ OOOOOOOOO oo O O O O O O 00 o . . . o o .
OOOQ O B o o o o o o c o o o
0 0 0 O O O O O O O O oo Q OO O OO O O O O O O O O O O O O O
OO O O O O O O O O O O OÏ oo ooooooo o o o o o o o o o o oO O O O O O O O oo o
O 0 . .O
................ o o o o o o o . OOOO.
. . 0.00000000000000000_ OOOOOOOO oo o o o o OOBBBB BOOOQOQOO ooooo o o o o o 000 OOOOOOOO O OOOOOOOO oo OQOOOOQOOOOOOOQOOQOO 0 0 00000000000000000000000000 o o o o o o o o o o o o o o o o o o o o o o o o oOOOOOOOO OOOOOOOOO OOOOoo o o o o ooo o o o 00 0OOO O OOO QQ 0 0 0o oo . . . O . . . 0 .0 o ................ : 111. 0 0 . . . 4 7 3 7 4 N 4 4 4 N
li
I i
i: I
• Mi , ;
i l
■ii!ill
t ; - : : - - : î î î î. . . . . T . T
I
. 1. .
I
IIi i i i /
3K . ■ p f i i i * » ,K K 4 4 N 3 4 1 1
4 . 4F ■ 7 4 4 K 1 1 1 1
K 3 7 3 3 1 1 1 1 . . T T
y-TTT:::!,-7 T T ! *. ! ' ! K K K K K .
T T T T T T T . K K K K K K K . .T T T T T T T T T T K K K K 3 K K . i \T T T T T T T T T T 3 K K K K K K K K K K K T T T T T T T T T 1 F K K .K K \K K K K K K 3 T T T T T T T T 1 4 3 K K 3 K K K K KT T T T T T T f l l . . L K K K K . 3 K K K K K ............T T T T T T T T T l I K K K K K K K K K K K K K K K K T T T T T T T I . K K K K K K K K . . K K K K K K K 3 . T T T T T T T l .K K K K K K K K K K K K K K K K . . T T T T 1 T K K K K K F 3 K K K K K K K K K K KT T T T T T W . 1 T K K K K K K K K K K K K K K K ............. ......................T T T T T T T T 1 A .K K K K K K K K K K K K K K K K K K 3 3 4 F F 1 1 1 1 1 T T T
....................................................... L K K K K K K K K K F K
I. . . T T T T T T . K K K K ..................
T T T T T T T T T T T T H K K K K K K K K T T T T T T T T T T T . P K K K K K K K K K K T T T T T T T T T T T T F K K K K K K K K K K K K
" " I I I ! ; i i m i
i i l i i ,MîM” KKKKKKK K ..T T T TTTTTTTTTTTTT
IL
ITTT
T T T T T T T T T ............................. K K K K K K K K K K K K K . . . TT T T T T T T T T . K .................K K K K K K K K K K K K K K . K . . .
T O T T T T T T T T . K K 3 . K K K K K K K K K K K K K K K F K . K T T T T T T T T T . K K K K K K K K K K K K K K K K K K K K K K K K K T .
T T T T T T T T K K . K K K . .K K K K K K K K K K K K K K K K . . .
K K K F . K K K
l l i i :
T T T T . . .T T T T T . . . . T T T T T T T T T K K K K K K K K K T T T T T . . . . T T T T T T T T T T T K K K K K K K K K KT T T T T T . T T T T T T T T T T T T . K K K K K K K K K K K T T T T T T T T T T T T T T T T T T T . ( K K K 3 K K K . K K K K K T T T T T T T T T T T T T T T T T T . . K ( K . K K K L K K - . K K K ..........................
" i i i l i i l i i i l i l l. T T l T T T T T T T T T T . . K K K K K K K K K K K . . K K K K 5 F . 3 K I I
T T T T T T T T . . . . K K K K K K K K K K K K K K F 3 P K K . .I l l l i n r i . . . . , K K K . K K K K K , ^ ^ K K K K K , P K K K . . .
, ...............KtRMRMMIlllllMllMHMMIl::^ ^ T T . . . . S K K K K K K K K K 3 K K K K K K 3 « 3 3 K K K K K .
. . . 3 K K K K K r 3 S S K K K K K K 3 e 3 K K K K . . . ” 3 3 P K K K K K 3 ..............................
i | | |T . : :
T . .
I
(, . . , 3 3 3 3 K K . 3 * J
7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7
l l l l !;; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
. . 7 7 . 7 7 7 7 7 7 7 7 7 . 7 7 7 7 . . . . 4 4 . 4 1 7 7 . . . . . . . . .
W \/ W WW
.w w .wÜ" i
wwww T W W ( . wwwwwwww
w wwww wwwwwww
. . wwwwwww
E W . T W (W(W( . . WW.
I w w ; 1 ! ........ W W W .. .w . T W . . . .
o
g_ J
u5• 4
lUce3u
o
53
f
• • • • • MM* • • • *
2* (c* 2* • • • J • ce f z H* e * • * • • * • ^ e e c f
I - • • : V j - ^ . î S t :
J f.«m m m m
CC*
. . . f . . c r r j c
■ • • • • • • • w* M" M'
“ e| | f5î c - • c e - C C Ç C C C ....................H-. ■ • ■_• -ilf II J.; : : • •
. . .. . .. . . . . . . .. . . . SW W S'dS'<S'4'4y-^W W 4'4S'<W -.# . . . »ws«:'4'<S'*sW '<y"<wW "4'4W "W W '#
ce c • - * c . . S"^S'< 'W S'W '4'y'dN 'y'^ '<'#4S'#w s ? e t ' t ‘ .
-h S-^WSSWSWS-^'4SSW'#y4S^-#-4 . S '# y " ^ S 'd W '4S 'yw y«4««S '4W ^ '# '# s
C . .
k . w -y '4 s 'y s w s w s ^ w 'w w w y s '4 '4 « « w w w s ^ y ^ s w s s " 4 w w w 4 s s w ' ^
- , . . . . SSSW S W S" 4SS "W '4'4 '< '4^W '4SEC...................WSS«WW'4SSW"<S'WS'4WSWWW'<.......................W '#4SW Sk*SSSS"^^"<*#W 'W '4'4-^
. . A A 2 Z'^•4' '^' '4‘ -^’é■ ' - 4'4' ' k M .» » ( x z z z w s w s s s - ^ W '# '# ' 4 '4 y '« . S W » 4 Z Z W S W S S S S '* -^ 4 '« -# '< '4 . W W W Z Z ^ -yW -4yS S '# '# -4 -4 -4S S -4S . . 2Z2Z'4-é-i'4'4'4'i-4'4->4'é'*'^'4-4'4 . . Z Z Z Z «4Z '*S '4W S'< '*S W W S-#'4W . . ZZ ZS'^W " <S '4 '#S S'< ^ W «#S'^ '4«#
. * * S '< S W k .W W 4y-4y#W k #-4S '* '< K s s *4-4 -4 s s -4'« *<-4-4 «< <<' I -4 *4-< s -4'< SS-4-4-4'4"4S'4-4W W '4S-4'4W 4'4'4'4'4 . S'<'4*4*4*4-4'#’4-4'4-4'«#-4-4*4«4'4'4"4*4 . -4 S -4 4 '4 « 4 S '4 S '4 S '4 W S '4 y y -4 '4 W '4
S -4-4 *4-4 S -4 *4'* *4-4 >4 *4 «4-< *4 *4 *4 "4-4 «4 - . ^•4-4S*4-4'4*4*<«4-4S*4«4-4'4'<*4'4S . .« * '4 . ■4*4-4«4'4"4. >4*4«4«4kl"4'4*4*4«4 *ZZ*klUUISüiUIUIUiUik4'4UUi •4'4*4
m m m uisuiu iu i u s -4 '4 a u iu iu i '4 '.^ 3 _ _ . . . . r . . . . =1. . . . . . . . . . . . . M. - . - — . -*. . - . - • > - * u « . . m u iu ia su ii^ o i u s-4 -4 a » * ^ » a -4 - . \
« 1» I* uii» m u u n i Ul t» I5 u 11 u iu Ul Ul m u u «1 m m m uni tl tim m m m m m m m m unim m m m m w m
unim m m m m m m m m m m m m m w m m m m m mtim rnmm m mwm m wm m m wm m m m m m m . . . . . . . .mmm mmm mmm m mm mm m m
mmmmmmmmw m m m m m m m m m iim m m m m m m »*- Z » Z Z Z Z Z Z Z Z -4 -4 -4 -4 ’4-4-4«4'4-4-4-4n ---- ------------ -- -------- m m m m m m »*- Z»2ZZrzZZZ-4-4-4-4-4-4-4-4’4-44-4v
. . . mmmmmmm s . 4 -4Z Z Z Z Z Z Z Z Z -4 -4 '4 -4 -4 '4 -4W -4 m mmmmmmmmmmmmm-4 » '4 Z Z Z Z » » » » - 4 y - 4 - 4 - 4 - 4 ^ 4 - 4
ZZZZ»»»»»» ^-4-4-4-4-4-4 ■4
m rnim m m m m m m m m m m m m m m m m m m . m m m m m m m m m m m tim tim w i»
m m m uim m uim m m m m m m m m m m m m m m »».^.^ . * ; ; * * f'f*; ! | | | * 27". " . . . . Ct ................... » Z Z Z Z Z Z Z » -4 y z 4 -4 - 4 .4 - 4 -4 .4 Sm. . mmm m m* , - 4 -4 Z Z Z Z Z Z Z Z W »Z S k4 .4W k4-4S
, W * 4Z Z Z Z Z Z Z Z Z -4Z '4k4 '4k4 -4k4k4S • 4 * 4 S Z Z Z Z Z Z Z Z Z Z » ‘4.4-4*4-4-4-4
• . • ^ S S Z Z Z Z Z Z Z Z Z Z - 4 - 4 - 4 - 4 - 4 '4 '4 . . . S Z - 4 S Z Z Z Z Z Z Z Z Z Z '4 * 4 -4 -4 -4 * 4 S • • • » Z Z Z - 4 S Z Z Z Z Z Z Z - 4 '4 S - 4 - 4 - 4 * 4 > 4 . . . w -4 Z Z Z W Z Z Z Z Z Z Z Z * " 4 4 S S -4 S '4
................ » Z Z 2 Z Z Z Z Z Z Z Z Z -4'4'4k4*4-4-4...................... ZZZZS2ZZZZZZZ't'é'4'*'*'*'*'*...................... » Z Z Z Z Z Z Z Z Z Z Z Z " 4 S '4 S - 4 '4 -4 S
................... 2 Z Z Z Z Z Z 2 Z Z Z Z 2 -4 -4 S -4 > 4 -4 S -4
. . . . » 2 2 Z Z Z Z Z Z Z Z Z 2 -4 -4 '4 S '4 k 4 k 4 . . ...................Z Z Z Z Z Z Z Z Z Z Z Z * 4 » Z S S S k 4 » . •
. : : : 5 i i i i i i i i i i l 3 i i 3 3 3 î . - * :................ - 4 Z Z Z Z Z Z Z Z Z Z Z Z Z Z ZZ'*'*' -
.............s z z z z z z z z z z z z z » » z« • •
................... - Z 2 2 Z Z Z Z 2 Z Z Z Z Z ' 4 ' 4 S -42 - -
................... S » * Z Z Z Z Z Z Z Z Z Z Z -4 k 4 * 4 S k 4 . . . ................-4 -4 -4 Z Z Z Z Z Z Z 2 Z Z Z -4 ’4*4«4'4. . .................... s - 4 m m z z z z z z z z z z ' 4 . •*• - u s . .................... - 4 Z 2 Z 2 Z Z Z Z Z 2 2 Z Z'*....................... ................ * '» Z Z Z Z 2 Z 2 Z 2 Z Z Z ' 4 - 4 ......................., C t‘ . - S Z Z Z Z 2 - 4 Z Z -4Z Z -4-4 . . . .
' . -4S Z Z m -4S »N -4 -4 -4*4 -4 -4 -4S N . . . . »W -4k4S . . . « - 4 . . . ^ . . . . . »
# . . # A A '4 '4 A » . . .
E -.
ytytpt. m^tJW .
cccccS ^
. . m m m m ^m j)
. . . . m m x m f -* . . . . mmmm -»
MM. MMMU)M ^.^M M M M M
FIGURE 15. FINAL Cl CLASSIFICATION MAPSECTION 12
54
A ccording to R eference 6 a m a jo r ity o f m i s c la s s i f ic a t io n and non
c l a s s i f i c a t i o n can be a t t r ib u t e d to weed grow th and low ly in g a re a s
w ith in d i f f e r e n t f i e l d s . This p ro b a b ly -a lso accoun ts fo r th e appearance
o f bo u n d arie s in th e f i e l d s p re se n te d in th e s e r e s u l t s . For exam ple,
F ig u re 10 c o n ta in s a h o r iz o n ta l ly p re se n te d w heat f i e l d n e a r th e bottom
w ith a m is c la s s i f ic a t io n o f o a ts in th e m idd le . T his m is c la s s i f ic a t io n
i s due to th e p re sen ce o f a low ly in g a re a . The bo u n d arie s in th e
d iv e r te d a c re s - re d c lo v e r f i e l d j u s t above t h i s w heat f i e l d a re due to
th e p resen ce o f a sm all sand dune.
I t may be o f i n t e r e s t to n o te th a t th e re a re u s u a lly more f e a tu re s
re p re s e n t in g a row crop such as corn and soy , and th a t th e non-row crop
f i e l d s such as wheat and o a ts a re more homogeneously c l a s s i f i e d per
f i e l d . This r e s u l t i s p robab ly due to th e sen so r having to average no t
o n ly over th e canopy s t r u c tu r e o f a row c ro p , bu t in a d d i t io n , averag ing
over a p e rce n tag e o f b a re s o i l o b se rv ab le between th e p la n ts . The type
of s o i l could a lso vary from lo c a t io n to lo c a t io n .
Y ellow stone Park
F ig u re 16 c o n ta in s a v ideo r e p r in t from channel 9 o f th e ground
scene on th e l e f t , a boundary map in th e c e n te r w ith th e lo c a t io n o f th e
i n i t i a l c l u s t e r s , and a f i r s t pass c l a s s i f i c a t i o n map w ith an a d d i t io n a l
s e le c t io n o f c l u s t e r s .
The Y ellow stone P ark d a ta was ana lyzed e x a c tly as th e Cl f l i g h t l i n e
d a ta . The v id eo r e p r in t c o n ta in s some ground t r u t h and lo c a t io n s of
t r a in in g a re a s used by o th e r in v e s t ig a to r s l i s t e d in R eferences 11 and
1 2 .
55
im
f ■ ■■
..o=C
‘i
4i
, Æ
FIGURE 16. YELLOWSTONE PARKVIDEO R E P R IN T , C LU STER SELEC TIO N , INITIAL CLASSIFIC A TIO N , AND SECONDARY C LU STER SELECTIO N
56
Table 9 g iv es th e merging p rocedu re f o r both c l a s s i f i c a t i o n p asse s
s in c e no m u lt ip le merges were en coun tered . No id e n t i f i c a t i o n i s g iven
f o r th e c lu s t e r s because th e c lu s t e r lo c a t io n s do n o t n e c e s s a r i ly c o in c id e
w ith th e t r a in in g a re a s , and i t i s e a s ie r to id e n t i f y th e f e a tu r e s a f t e r
th e f i n a l c l a s s i f i c a t i o n . The a n a ly s is o f t h i s d a ta s e t in d ic a te s th e ty p e
o f problem invo lved when a f a i r l y in a c c e s s ib le re g io n i s rem o te ly sensed .
I t i s d i f f i c u l t to e s tim a te what ty p es o f fe a tu re s can be e x tra c te d from
th e d a ta and i t may be econom ically to th e advantage o f th e in v e s t ig a to r
to c o l le c t th e ground t r u t h in fo rm a tio n based upon th e f e a tu r e e x t r a c t io n
map, r a th e r th an t r y in g to a n t ic ip a te th e needed d e ta i le d ground t r u t h .
Table 10 was p rep ared fo r in t e r p r e t i n g th e f i n a l r e s u l t s based on
in fo rm atio n d e riv e d from th e v ideo r e p r i n t . S ev era l meadow l i k e a re a s
w ere d is c e r n ib le , b u t were only g iven meadow numbers co rrespond ing to
t h e i r c la s s numbers because of la c k o f o th e r in fo rm a tio n . The g eo lo g ic
term s t i l l , t a l u s , kame, and v e g e ta te d ro ck ru b b le a re d e sc r ib e d in
R eferences 11 and 12, b u t a re re p e a te d h e re fo r convenience.
The c la s s t i l l c o n s is ts o f meadow a re a s u n d e r la in by g la c ia l t i l l .
They a re g ra s s la n d and sagebrush a re a s which were la rg e ly dormant a t th e
tim e of d a ta c o l le c t io n . M ineral s o i l i s exposed in about o n e - f i f t h of
th e a re a and c o n s is ts o f s i l t y to b ou lde ry d e b r is . Deer and e lk manure
a re lo c a l ly abundant in th e se a re a s .
The c la s s ta lu s in c lu d e s b lo c k f ie ld s , t a lu s , and ta lu s flow s o f
b a s a l t la v a f lo w s , v o lc a n ic t u f f , and g n e is s , formed by f r o s t - r i v in g and
s o l i f l u c t i o n from o u tc ro p s . They a re b locky and w e ll-d ra in e d d e p o s i t s ,
and t r e e s a re w idely spaced o r a b se n t. The b locks a re covered w ith
dark gray lic h e n s and range from a few c e n tim e te rs to about 1 m eter in
57
TABLE 9. MERGING PROCEDURE PGR YELLOWSTONE DATA
CLASSIFICATION PASS 1-10x10 ARRAY CLASSIFICATION PASS 2-6x6 ARRAY
INITIAL CLUSTER NUMBER
FINAL CLASS NUMBER
INITIAL CLUSTER NUMBER
FINAL CLASS NUMBER
1 1 11 11
2 2 12 11
3 2 13 11
4 3 14 11
5 3 15 11
6 2 16 11
7 4 17 11
8 4 18 11
9 3 19 11
10 4 20 12
11 4 21 13
12 5 22 14
13 4 23 14
14 6 24 15
15 6 25 15
16 4 26 16
17 4 27 16
18 4 28 16
19 4 29 16
20 7 30 17
21 8 31 18
22 9 32 19
23 10 33 19
24 10 34 20
25 10
58
TABLE 10. INTEEPEETATION OF YELLOWSTONE RESULTS
CLASS NUMBER SYMBOL BRIEF DESCRIPTION
1 1 MEADOW 1
2 2 MEADOW 2
3 3 mADOW 3
4 4 DENSE FOREST AND SHADOW
5 5 TILL
6 6 KAME
7 7 MEADOW 7
8 8 MEADOW 8
9 9 MEADOW 9
10 0 MEADOW 10
11 A TREES
12 B TREES
13 C TALUS
14 D TILL
15 E TILL
16 F TILL
17 G TILL
18 H TILL
19 I VEGETATED ROCK RUBBLE
20 J MEADOW 20
59
d ia m e te r . Most a re l a r g e r th an 10 c e n t im e te r s . The s lo p e s in th e se
a re a s range w id e ly , from 35 to 45 d eg rees a t th e head to 5 deg rees o r
le s s a t th e to e .
The c la s s kame i s v e ry s im ila r to t i l l excep t about o n e -fo u r th o f
th e a re a i s exposed m in e ra l s o i l .
The c la s s v e g e ta te d ro ck ru b b le c o n s is ts o f lo c a l ly d e riv e d an g u la r
ru b b le , f r o s t - r iv e n from b a s a l t la v a s , v o lc a n ic t u f f and b re c c ia , and
g n e is s . G rasses , l i c h e n s , everg reen s e e d l in g s , and mosses cover more
than th r e e - f o u r th s o f th e s u r fa c e u n d e r la in by th i s d e b r is . The rocks
range in d iam ete r from le s s than 1 c e n tim e te r to about 1 m eter and occur
on s lo p e s from zero to about 25 d eg ree s .
Three a d d i t io n a l ly known f e a tu r e s in th e ground scene d id n o t appear
in th e c l a s s i f i c a t i o n map because th e y were n o t co n ta in ed in a homo
geneous a re a la rg e enough to be s e le c te d b y a c l u s t e r . These f e a tu r e s
were w a te r , bedrock and bog. However, th e a re a s where th ey appear on
th e c l a s s i f i c a t i o n map can be lo c a te d w ith th e a id o f th e v ideo r e p r in t
and th ey appear as u n c la s s i f i e d a re a s . These c la s s e s could now be
id e n t i f i e d elsew here in th e d a ta by u s in g a su p erv ised tech n iq u e and
s e le c t in g th e se u n c la s s i f i e d r e s o lu t io n e lem ents as t r a in in g a re a s .
F ig u re s 17 th rough 28 co n ta in th e f i n a l c l a s s i f i c a t i o n r e s u l t s
fo r th e Y ellow stone Park t e s t s i t e and F ig u res 17 th rough 22 co rrespond
to th e l e f t s id e o f th e v id eo r e p r i n t , w h ile F ig u res 23 th rough 28
co rrespond to th e r ig h t s id e .
I N0I133SdVW N O I lV O I d lS S V lO M U Vd 3 N 0 1 S M 0 1 1 3 A 1 V N I J LI 3 U n 0 l d
tvr\.q * i< g < a a ia a a a « a a « a
• /« fX iU A A W W Q e U U A A O A - • A A A Q A A flA U < A < t a « iA a A a t t a « L a a a a a A A a A q A A a a t t A O A a f t m a
'kt.NfVU
urvo J J t J 3 JM<NJ J J J J
J J J J > J : . 2
«AAaaUAAAAAAAAa Ii awAAAÂqaaaaA •
MANM<U\a«iUA4i/M\2\M.AAAA 41~.r 'rN/\2\r\M«4A«iUai4.\Ma<i«l2NMAA«l<lAATA
.wvuvAUMuwt <\rvrvMq<4 «iANrvAAUAttauqAAAAaA ojaaq qA,a aq<QA«ia a a aa a a AA a a aaa a AAaaaaaa2 f y\ N2UA/\AAAAqAAqAAAqAAAaqqAQAAaqqqaAAAAAAAAAAAAAAaAAAaaAAA
>\ru\ A aAAaAAAAA AAAAAAAA AAAAAA A»iaqAqaAAA AAAAAAAAA AAAAAA •\ xf\A 12 — A AAA AAA AAAAAAAAA AAAAA AQ AA«1A AA AA
• \2\ \r-<M>tS2NAAAAA AAAAAAAAAAAAAAAAAAaq AAAAAAAAA AAAAAAAAAAAA AAAA AAM<\ A/v vrxA— AAAA ' «VAAlMAA
AA AAAAIXAA— • f\AAA - - - - -. - —-2AAA AA ■ - AAA - '-.>■<% AAAA . . . AAA
• ' AAAa<\M 2 AAA ' —- AAAAA <—*%-<\2NAA 2A/VTV■ I AJAAA-sr«/W «\2NAA fVAI 3AAJ JA—r r — A37rw2\. <%
AiN>3AAAAA2A <NJ rv. 3 2 «< r» «NA7 AA - - . AiV. ' . ■ AAAAAAA A AAAAAA Af\ 3 AAAA A. . INATA3AA . . AA - • <\AAAA A • AAAAA AAAAA AAAAAAAAAAA
A TAAAAAA.AA 2 3 3 , A ..................AAAAAA A AAAAAAAAAAAAAAAAAAAA .. A 1 A r\ AAAAAAAA 3 3 3 3AA . . . . . . AAAAA AA AAAAAAAAAAAaqAAAaqAA
I 2 — .3A 33AAAA3 3A3JAAAA..........................AAAAAA 4N. AAAAAAAaAAaAAa aaqq2 2 AA2SMA3 3 3 A fv 3 AAAA . AAAAA fN . . . AAAAAAAAAAAAAAaaqA22 A <N2\rvfN- A2V2\2Sr>. A333A 33AT33 .3AAAAfA-T ■ ■ AAAAAA . f-AaAAAAaa AAAAAAAqA
2 2 -VA f\2\JVAAf\2\A Ow3 33333333TA AAAAfs/*.» r AAAAAAA «% f-f-AAAAAAaqA A A,AAAA A AA2 2 3rv I A rviN. . f\ . _ . AA333333 AA <\2N. . r r ■ AAAAAAA . AAAAAAAAA • • ■ AAAAAA •
2 2 2 2A r\2V3 2 3 3 3f\2V-<WV\ (V — .3A3 3 33 3 3A . CVA ■ r r AAAAAAA AAAAAAAAAAAA • "-fVAAAA ■ '«V UA 33 3 rvfv. . . 3 AAAA fk. AA3 A33A —fVfVi—r\J-.rAAAAAAAAAAAAqAAaqAAAA . AAA
2 »\ 3 3 3A 3 rv3 OAAAAA rvU A3 3 A-\ p fV\r rr — AAAAAAAAAAAAAAAAAAA<\. . AAAA2 <\Tv 2 3 rv2V . A «N. AAAAA <V A 3 3 3AA A ■ ■■■... . — y\fv\A AAAAAAAAAAAA AAAAAA A AAAAA2 2AiN2\p3W\A <\f\#-AAAAAAAA3AA — J3AAAAAAA* r ' fsfS/VAAAAAAAAAAAAAAAAAAA A r ■
2 2 <VU A AAA AAl\MAAAA3-i<NAA3A .3 3 33AAAAAA2» Al\r—f\g\r\AAAAAAAqAAAAAAAAAA . . <*AA . . 'A <-s. A2N. A AAfV A <Nf\. A A333 3AAAAf\ A «\P3MU AAAAAAAA AAAAAAAAAAA . . . AA ■ ■
1 3 fx 33 33AAA3-3 f\. rs. 3A3 3 3 AAAAAA AAAAAAAAAAAAAAAAAAA . . AA <• ■2 2 3 . . . — . 3 33 3AAAA <\fkf\fA333 3 3 3 3 3AAAAAAA2N|\iN2Nf>2Nf>3\AAAAAAAAAAAAAAAAAA ■ AA . r r r r2 2 2 >3 32 IN . 3 33 33AAA333 33333333 3AAA 2N. f\fvfV3Nf\f\2\2VAq A AAAAAAAAAAAAAAAAAAAA . r r r r2'W \3333 <\f\ 33333 33 333333333 333AAAA-, AA~4VU2MV AAAA AAAAAAAAAAAAAAAAAA r r r r rrj*. 3A3 3 3fV\2—3 3 2 333 333 3 33 3 3 33AAAA—r AAAAAAiv/nAAAAAAaA AA AAAAAAAAAAAAAi r r r r
rrrr^—r r r r r r r r f r r r r r r r r r r r r r . r. <*f'f*r'i"2»f»r» r r r r r r r .
r r r r r r r r r r r r r r r r ■rr rrr rr '
r r r r r r r . ■ • r r r r r r r r r r r . r r r r r r . r rmpr
r,<•2*1* r r r r r r <*rr»f'. r r r r .
r r r . ■ r r r r . r r f* r* n 2* !<• 2* 2* r» r 2*2» 2* f* r
r r r r r ~ i*2»2*r2"2*r2*2*. r r r ■ ■ »*2*2'2'f'2»2»2* . . . r r r r r r r r r
2 2 2 2 2 2 2 2A3 3 A2\WA JA2\2V 3rv AAA3 3 3 33 3 3 33333 33333AAAAV • Af\f\ AAAAAAAAAAAAAAAAAAAAAAAAA c m r11I 2 2 22A «- 2N2S2NAA2 3 3A3 3 3A fv3 3 333 3 33333333 A3333A A . ■ . o r p-AfV AA2\AA AAAAAAAAAAAAAAAAAA r r r r r r1 IA 2 2 2 J Arv3A>\2V2N3'M\A3A3 3 3 3 3 A3 3 3 333333 3 333 3A3333333 •- —— AA2\ 2\jAA A AA A AA A AA A AA A AAAA A AA A r r r r r r2 2 2 2rv2N2\2N 3AAT2\2\ A3 33 2 3333A2A333 3 3333 3 3 33 3 333A r&fs. r. AA 2\AAAAAAAAAAAAAAAAAAAA r r r r r r r r•113a \2\.2AA •■.»* AAA33A 3A 3A J 3A3 3A3 3 3 3 3 3 3A 3 3 A 2\2V . .J A 3AAAAAAAAAAAA AAA AAAA • r r r r r r r
2 2 3 1 AAA A AA . 2N. AAA . . ■ 3 33 33 3 333 3A 33 rvr. <N . . AAAAAA AAAAAAAAAA AAAAAA . r r r r r r -2 2 2 3 2 ATM AA *. — — <V_1 2 A 3AATA. ■ A 3 3 3 3 33 3 33 3AA3 AATJN r r p> AA 3 A AAAAA AAAAAAAAAAAAAAAT r r r r r r r -2 2 2 2 2 A 39 1 .— A-fWA3 9AA3A r r CN3VAA33 3 3 33 3 3 3 33 3 JA3>H% r —r3\ J 2 3 333 3AA AAAAAAA AAAAAAA r r r r r r r r r r '2 2 2 3 A <v /\rvAAAAA r r r Ar2AA33^3333 33 33 3 3 3AAA 2 3 3 3 3 TAAAAAAAAAAAAAAA r r r r r r r r r r r r’ 2 2 2 1 A -\AAA.\r A A «' : ..33AA3A3333333333333 f\AA3333AAAAAAAAAAAAAAAA r r r r r r r r r r r12 12 2 IWAAA2 2 —rvfVMA . . <\«3 3 3 33 3 3 3 3 3 333 7 3 3 3 3 3 3 . <vr\,-AA-AAAAJ 3AAAAAAAAAAAAAAAAA r r r r r r r r r r r2 2 .2 1 r\2*»2V2*\ 3 — rjv —f\A r A 3333333 2 33 333 3A3 3 3 JAArjVj ■' ■■ i\AAAA3AAA TAAAAAAAA AAAAA A.-r r r r r r r r r r r2 2 lA*. 2 fVA— --r3\2Vf\i-4i>,r <\ 3A33333 3 73A33 A3 3 3 3Af\2\AA. . f\. A3 3 AAAAAAAAAAAAAAAAAAA r r r r r r r r r r r rAAA I A3 —4^1 333333 3 33 3333 IN. Ou3A AA3 33AAA 3AAA AA A A AAAAAAA r r r r r r r r r r r r r .
«. — 3 3 3 3 3 3 3 3 .33333 3A A AA 3 3 A 3 AAAAAAAAAAAA . . . r r r r r rirr r r - - '_ r. — - 3 333333373333333 3 3A A AAAA3 3 3 3 3AAAAAAUAAAAAAA . . r r r r r r r r r r r .
i r n . . AW 3 2\2Vf-«\ — fVAA *N 33333332 233333333 AA2VMN 3 A3 333333 TAAAAAAAAAAAAAAA . r r r r r r r r r r r r rs* AA A *4 — NAAAA 3 3 3 3 3 3AA 33 3 333 3 7 3A f\ AA A3 7AA A33 3 3A AAAAAAAAAAAA r r r r r r r r r r r r r r
_ AAA 23333333 3.T 33333333 . - AA 3 3AA3 3 AAAAAAAAAAAAAA r r r r r r r r I* r r r r r r . AAAA'\ 2 .3.2 2A AAA3332 333333 3 3 23333 r3N2V2NJN 3 3A3 A 3 3AAAAAAAAAAAAA . r r r r r r r r r r r r r • • AAAA
.222 133222222 3AA33 3 33 3 3A <N (A3 333AA3 333 (N2\f\r,—T2\A3 3 3 3AA3 3 3AA AAAAAAAAAAA r r r r r r r r r r r r r r A A332333212223 3AA2 3 3 33:3 N A3 3 3 3 3A3 3 3 3 3 r\. . , W rvfv 3 3 3A3A3 3AA3 3AAAAAAAA A . r r r r r r r r r r r r r r r . — AAA
r r r r r r • r r r r r r r r r r • ■ *— rr rrrr
r r ■ ■ ■ r r r r r r r r r r r r r r
r r . r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r
• r r r r r r r r r r r r r r r ■ r r r r r r r r r r r r r r r r
A r r r r r r r r r r r r r r r r r a, r r r r r r r r r r r r r r r r r i-r r r r r r r r r r r r r r rrr r r r r r r r r r r r r r r r
. <*r ' . r r r r r r r r r r r . . r r r r r r r r r r r r r r . rr rrr r r r r r r r r r r r r
r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r . r r r r . r r r r r r r r r r r r . r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r . r r r r r r r r r r r r r r r r r . r r r r • r r r r r r r r r r r r
. r r r r r r r r r r r r
. r r r r r r r r r r r r r r r r r r r • rr«- r r r r r r r r r rr r r r r r r • (srrr r r r r r r r r rrrr
222322223223 22332233332122222 I 1232222232 <22322/ 22232)223322223223 2223221233222)3223 2223322232 I 12 23232 322331222)227.1 3221 2 : 2 1 2 3 323 ) 21 : 2112 2 2/222322222.* 222 122
A.T3AAAA1N 3 73333V333233 A <N33 3 3 3 3 3 .
3 A «N1N 3 3 33 3 3 32 3 <N2V 7(N(N AAA 3 7A 3 3 3 —
J n—rvr 3 f\2NA3 A (N>73 23 J TXrVtNj Ar»f\2N,-lN7 3 3 3 (A—<N2 2 2 vJArsrv/NArcsrs/SA A33 A ~
—<\3A2\2\rjNrs2\'N/VA3 3 3 3A/N2S —<\A AlNfvrrW A2 33 3 r\2N - .-VTV (NIMN A3 3 CNN
2AA ■. ■ . ~-C\rMNATv AAA <NTV:322232223322) 1 I2222A . ■ ■■ (NIN . 3(N337332321333223122) (NINT ——»f\rvrvfNr\<-rvAA3 3rs2*>
23 2222223321122)3 AA -e.<V\r — •»*t- AA <N22 \U 23 2 2 222 22 22 233 N, ................... . (MNAAA*(N1\ 23)1323221 1 2 A- - AAA•\fNC\t\ 1 2 2 2 3 3 2 2 \l\f\ 2«\f— fNw rVJNAA—<V —<xrrvfVtVJ 2 1 2 2 2 l«fV(\f\ - — - —(NfN, . . . — .3 Nf\lS f\•xIAVtv 3 3 2 3 2 Nl\ci\A. ■ ■ — — — p\jNJA- \r. — (N
3 2 13 \(\rvl* p.23 2 2 *Nr/\2\/\«*l\<-p—p—^3 2 \lNl\(VfVf\f\;-—.. — p. —#-p.P-f\r\p- AA * —
' 2 <“*N/SfM\nv —P..P - <NfN AA«4.p<fvr\^p.<\f\pp(N»p^^.p ■ I ippi. ■ f .fA V p/A A ^.
AAA 7 7AA7AAAAAAA AAA IN A7AAA A 3AAAAAAAAA . . r r r r r r r r r
(M»> (Nf\AA AA 3AA AAAAAAAAAAA . r r r r r r r mIN p\a a 7AAAA 77AAAAAAAAAAAAAA r r rrrr rr /* / p-r f AA AA 3 TAAAAAAAAAAAAAAA r r r r r r r r r r rs CAAA3 3AAAATAAAAAAAAAA r r r r r r r r r rr\ _<v AAAT TAAAAA* A AAAAAAAA r r r r r r r m
Nxv.- AAA33AAAAAA3A<-. AaAAAa r r r r r r r r r / f . r . A 3 TAAAAAAAAAAAAAAA ^ rrr rrrr r
AA 3 AAAAAAAAAAAAq AA . . r r r r r r r r r NiNf /mnAAaaaaAAAAAAAAaAAAA r r r r r r r r r r
N r\r\A AAA AAAAAAAAAAAAAA A «-rrrrrrrrr Np- «N aaaaaaaataaaaaAAAAa r r r r r r r r r r — p\ . AAAA IN AT3AAAAAAAAA r r r r r m rr ■..r. AA AT3N AT AAAAAAA r r r—«NT- «N/V A CVANAAT AAAAAAAA - rr ,• lAMN NIN rrA*;-AA 7 TA AAAAAAA - rn
— N2N p. /Np-r. «NAA3AAAAAAAA rr rr\r\ rrvp. . AAA AAAAAAAAAA r r r r
A rr rvAAAA AAAAAAAA r r r r<Nr\ ’*rv — iNAAAAAAAAAAAAr r r r r r r r r r r rA — '• pptv/nAAAaaaaaaa . r r r r r r r r r r r r. p. AAAAAAAAAAA r r r r r r r r r / rrp-.-r\ pp. <■. AAAAAAAAAA r r r r r r r r r r r«•«— IN/VA iNtSAUAAAAQAAAAA t-1-r m ' r r r r
.pp. —/\(Nr. AAAAAAAAAAAAAA r r r / r I r r mr^p-r A aaaaaaaaaAaAA r r t'r !• r I'r r r r rrp—r IN AAAAAAAAAA r r r r r r r r r r r ri. pppp iPpi p-r. —IN 2AAAAAAAAA r r r r r r r i ' r r r
p. - — — —IN AAAAAAAAA r r r r r r r r r r r.~~.r\AA « /\/pf\,-«p.rpAAAAAAA«*AAA r r r r r r r r r r r
" — AAA.." r* A AAAAAAAAAA r i r / r r r r r r •N/N AAA AA AAAA < i r r ( r r r— p. «V AAAr A A aAaA | ^ r r r r /'r /■
•Kl nil «I llltllilK AN A(.1I(AC.<1<2 a'lAAAAA
• r r r r r r r r
r r r r r r r r r r r r r
r r r r r r r r r r r r r r r r
r r r r r r r r r r
r r r r r r r r r
09
ÿ N0I103SdVW NOIlVOIdlSSVlO MUVd 3N01SM0113A IVNId QZ aUOOId
• . 4&aKi% om - •■ T ^ a a ïQ A Q A a a ■
A A J A A A A A ft f t A M A A J A A A O A A t t • W U '
•MMMMMUMf
£9
64
11 r
▼H>T*»* •
T*T»»t*t>
T>TVT»T>T*t>>TST> «T»T»T>t*
tl T»T*V*T*M*fi- SV »»P«iVl>1>t*•»T>T.T*T»T>»*
*» Tyr>r>T>Tv • -T>T» T>T»t>T»V»T>tV t '
»»T»T»T»T»
I n». »*t» i»t» r cT»TvrYkWT>m»«T>T» n»I rm ?»T»T> T>t»T>WT»T»tM»'t»T*T>^T* t * »KM». *» T*W»T»nT»X»*T»T*î»*>t»t*t*T*T**WT*
r» »»T>T> T*T*T»V»%J f 1* •T«T> TST* • -
T>T*T»t*WT»T»T» T»T»T»T»T»t»t>r>T>T»T» r**»r»t»T»*»T»T> t»T» •*r*T>TVT*T*T»T»t*T*»»T» •
t*>p •T»t» T»fr'»*T*T»WT»T»t»t»»»T»»*T*t»T» ' ' \ f
T*1>WBT»WT»W»WT» • ▼>tV •
T»»>wr»r>w^rT»WT»T>*>T»»»t»ï> T»T»nT*W>T»1>T»T»ttT>T» T«T>T»»»f 7»TyT»T»T,«sT»-*»T>T»T»T»''»T>»VX t>T>Tsr>T>T»T>T»r T>r*»>T»—
^T»rr*»T>T>T»WW»^T>T»l»TH>T>T»T»T>t*W»*»T> »T»r>T>T»T»T»T<r>TymVT>*>t» T«*T»flST»T*T*>*t» t T»T»T>T»T>T» *VIW*T»T»T*TI**V, "
TyT»T>T>T>tyT> ^r>T>T»T>f T>T*T>T>T>»*T>*>'t>T»^T»T>T>T»T>T* t »»»>T>T»r»T»T>T»T»t>r.*ïT»T>T»T>»* - *»*yT»Tyr>T» »»T»T»T>rf»TrT>T>nr*'*>T»T>’Y'j>» t '>
T*T»1»T» n*» ^ T>TrpT>T»T>r»T>T>T» r\ tr»T*T*^T»t>»»T»T*T»T» T»ry»T»T>T» *>T*T»-4^ f» » "X».
• T»T» X*»» nrrmi*» -t> T» 1» *»v* j« t t »»r*
»>T» ' '•'> *>T»T»t> V» tr ttrrrtê/.
^ T t ^ r t ‘r»T> —.^ im*nr‘. *>r»>-»«>T>T» T»T*«* - f I r , , ,«
T>*« *»?*•n W»*SŸ*
»«•>»*•>** »>?»»>«>’>»>»>»***»*”•
T> *»»*•*•>*>»»» T* •»»* F» r» »»»*•»»•»»•'••
mv» ■*»T**1** F»T>t>»*»»F*F>»»F>»ir*F» *»»»»»T»T»T»»*»»T>T»r»F*r»F*F*
tu k n n » u » .
i n i .J in » tKrvnrnxT
t fvn,rrf»rt»v»*
FIGURE 21. FINAL YELLOWSTONE PARK CLASSIFICATION MAPSECTION 5
66.»S7\TVJM'
x iM \ j\ jM \ i> ju \J v * \< r I- 1%, r r r te c c yj\> . r r e t r r e r r r t r f f t r
r r r c t c r r c r c c t r t
r f s- V»'. Ni\i\»\jM\jvi'0'j\ro\J\JV)>j\»jVMNr\ju
r e p\rj\> r e t c e t r f r \j '»r c c- 'Js> r r f f f f ' ^f c rsAi c 11 r f e t c Ni r r r r i f t M v r t r r f
r * njsinjr r \ i v f \ f \ 't r \ V t t rsJN'f
r f fsf'^C rI V» t
r r \jM'iNJsJMNTON/vi r t rf \>- t
V.
t «ïsj'iv \.r\j\j\ro\jvj\ro\rNJvrg\»>j>jN 'J\j'jN> NjNfxjx' -.- ► NfV# \r\>\rJONJN.'NIN.T\»NJV»-^'0\ra\JNJNJNJV»>J'i\>\»\INJ\J>JMN*MO fMSJ-OV«\<
\iv~ MVj\j\»NJ\J\l\>\>MV'O\»\»Nr>J\JVJvJMNJ'O'J\JNJ'J\>VI’0\;MsfV M\> r
_ . [ , \>MVJ\lvJ\JV»\J\»'>MXJN»x>M'XJXjN.tO\IXJ'ONJ\JXJNJ\J\I\»V3Njx.*V> f f f
. - M \jv j\j\i\j.i\r\jM v i'jM v> v i\J \jN j\> v>\>«Jxr\-N i\> s js» \jx jN JV - xjsjvrv» i• NjM'*v>xj\j'xj\«'oxio\i>Jv>sj\iM>owxJ\iv»Njx» '«MX, ' \)\,f r r f r I -njnjmx» r r
,, r\JMv.-vjxii f,.-Aj-oxj\jN»Njs> r r r - r r r r r r •jxjx.r r t--\j\>--»rv»xjvj\/c r rvNJN»\Jxj'ir e r r ' . r c t t t r r r r r r c r fox-»'j'T r MNJMX» r r \i\jx »%r ■'* * ' “
•t.i ‘sJSj-> v fs jc r s j f c r "V r
Nr»»»»r c r t r rxjxj
r r .' r t r rv>—'j x>vr»r r c r r r r r
r»r t r e r t ' y j ^ r i»»f
rx fx» 'fx»vrv i\rN f\» \ \r\rxixfxr\iiv Nrxjv V \^\»\i\»xj\FM \rxf\r\/M \rN*N»»» v»\
xrx>o-i\r\r\j\rv\/\*vrx>x>Nj xfx rv>r >v ivrvr.;f >i\>Njvr>)vi\jMxi\r\txJvixrv>vrMxrxixfxjxj- <\.
- XI : > x iM \r \ ix r x to \ f \ r v t \> \ j* iv\« x r\* \) \r ixixi •ix}x>xjx|x<vj\rvixixixj- \r\
fJOOxrO -> •XJxlvrV»X>\JXjXjX»Nf'»x»X»SJXfXt\fv»Nrsj'JNfx»v>\r\ixixr'>* KiM \jsrxrxi\f*JMx»s.
c r / f c t »\»\r\rNj\»\J\iNi\jo\j>js»\js«s/'*\jx»>j\f>jM\r t 1 1 f r\r\»\r\f\f\*wi\)xr\fxr\f\i\.*xixfW\,xr\» rxjxiv.r t r c f c r * r- \rs/x»v'ixjxi'j\j\* i\j\«v\rx*\jxr\r»fv
t f \j\jv\r\f\r\rw\«\rx)\f\j\r\rx' vi\rv»\, \rvf\i\isivjoxrxfvt :xruxr\f-fxj\ ixjxrx.
f >js.‘ sjvjxi\KJvi\l\J*J\r<irx.xJxJWA. r r\*\» \jvjo'jxj'j\fxj'Osjx> - sTMx.
r e r *- •i\jv»jxi\rMxjux^ -. x. x.r i c r r r e t r ' r\f\*vxr\j\f\i\ xixrxj\»xfx*.wx.fxixrxr\
1 •'o vrx ix jx jxxos ix jx j- • x » \r> ir - jw x jx jx ivr c t c r r r t e c ' \rxjw\jxr\jx/xrx>xj\jxj>jx .r>jxrvix.
fxr'.rx jN fx i-ijx jxJs jx jx jx rx ^.ixf.ixr r •'»x>x»xjx jxr\jx j\» \r- »m v .P MvrMxrvlNjXJXJMxIxJvflv .,.1 I I.
i r r r r r r r r rc r r r r r r r r t r r
r c t c c rxj r r ev c r r r r r c r f f\r
r c r r r r c c r ">*»"> t I r r »x*x»»»x
c c r\»f-xj\rv
— f c t c i c r x;x) f ( t x j-.rxjxjxr — w v rr c c t r r 'J x>xj\ j \ p —
c r r r r c r \rxrx)\rxr\J\r\rvxrx,\jxrxi\r\r\rx r r c c I c r c*vjxjNJxrNrxixjvJxjxJxjsjxjxrxrxjxrvi ' <
r r f f t c r-'J' 'x7xj\jxr'oxjxj\rxjx»Nrxrxrxr\rvxjx) foxixrf xj r t f r r c t r r c fxjxrxjxrxpxi.ixrxjxrxJxjxJMNrxjr T*VTx c c t c r r r r r c c*xixi'J'ixtsrxi\»xr\jvrxjvjxjxjxi'j t rr Tx XJr e r f c c r r r r c c ">xjMNj\ix>\i»)xixrxj'r'<f f-r \rr r r 11 c r c r^ w -x t : xjxrvx. x, Mxjxjx-t t « c r r r xjxjc c t c r c r-xiMxrx>X’~. r x. p xj - -r cr r~ r c r r r t c r rxf\r v»x- : r r rr r r r * **xjx» x r r r r r r c r c r c t r r r x, x. p r 'x, r r t r t t i s f c t r r r r c r r c r- xjxjxjxjxj r t>c r r r c r c t r r c c- rr* r r c •xrNjxr—rxrxx i.ixix,»»*»'-» •»
r r c r r c c-vj c r f- t x - r xjxixrx»---» »-x, m»*"* «*«x j r f f x r - XJT» c *ox» xjxrxj — •-» x jx jx . *x
p»r "XXJxTXIx .r r x rx f x .v ' '
f«. / rxx»pxpimc **r*r* r ** r r r »x.* «xT»T»Tx«xr p>w«»»»x -xm, I r t r.» fxfxfxTXTxTxPxvxrxvxfxxrxM»» r f r r
***x»*»xT»n r f r t “•r I I
»xi"»*»T>tx»**x»*»x*,Txr r*sf r r fp**»T»r* H»vt> f r f I »X I t
t> n»»»>»xr. *>*xf r »x»x*x»» r »»
»xTxixr>*v *x x>fxT»t>»s^*x »x»x •XPXTX *•»»»**»
FIGURE 23 . FINAL YELLOWSTONE PARK CLASSIFICATION MAPSECTION 7
68
T>T>T*^r>T>»>r>T>»»T>T»
»>T>T»»VT*T»T»T»■nrtT*ryr*Tty>r>
T*
T>T> ••»»T> »>»T>ttT>T>V ny» T*'bT>T>T>»T»
•*>T>T» *>t> »t>T>f CT»T»T»T»
t*T»
T*^T>»t>T>î>T»
yy y»y>y»yyrwr>‘r>T>y>y»‘T>
f*
y>r>r>y>*>y* ■»*»
•»-»->■>-ï"» *rt r tv rv n f I
r. •> - y t t y n '
-yT rrr *»*»■» T •»•»*»*>*»■»» n TiT ■» «r-». f »■»■>» r-»•»*> tt •>
> f.
titvrvfv»' r. ti rt.n.rvrv>>
r» n j» j» .fv rt.
r» r tn n it . r tn r r r>
rvr n.ntnrtj i wn rvrvnA nT j»»n »» «
nr»», trrnrzt f.
■» ■jTT'jTnriT
e £ T»»»T» *>•»> r r»»T>-nr»t>T»T>»>Tk£
^ r»A£>»£T»«»r r i» T » r*> r-
T>T>T* T»T»T» »>T»T»T»t t-1 T>*>»>T>T>T»T»»»T>T»T»f r fT»r»1»*»T»V»T»T»*>T»AC £ r *» r A
T»T»*»T»*»T»T*£ f*T*T»T»*sT*T,V*T»A f *1 »»»»»>»»»»>**» f T)
— »»— C I rt***»»>»»£ n *» A yy » « r £ r
^ •«»»££*»£ A t > * s f t r r•>■»» £• V* I r’> r r c r » > A »>*%»>»* ( f t
fi -y y%t r C C C yyyyyy
, ■ —/ T>£> £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £► ^ - f j v r £ t £ £ £ c r r f f £ « e r £ e c « c £-W • • T » T » % £ ' r t £ C £ £ £ £ £ £ £ £ £ t r f f £ f
■ • ' £ ( £ £ * £ £ £ £ £ £ £ £ £ £ £ t £ £ £ £ f £ f~g— C C £ ( C r - C £ £ £ £ £ r £ ^ C r £ £ £ £ £ £ ££
-«r«J 1 V C £ £ £ rC % £ £ £ £ £ £ £ '■£££££■ £££££■ £w - £ £ £ £ £ £ £ £ £ £ £ £ t £ £ £ t £ C £ £ * £ £ f £ r
- • £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £- ' £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £
• • % £ £ £ £ £ £ : £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ ( £ t» t»£ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £
• T>T>T»t £££££££££££££££££££££££££££££ T > r . T > * * £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ * > T > r > C £ £ £ £ £ £ £ £ £ £ ( £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £’ - - ' £ £ £ £ £ t £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ r £ £
T» ££££££££££££££££££££££££££££y>T> c t e t t r c t e t c r e t r e r t c e c r t e t e t t t e e
»' T>T»T>T»£ r £ f f C C f C r £ f r f £ £ F £ £ £ £ f £ C r » £ f £ £It. **nc r £ £ £ f £ £ c t E £ f t t f r £ £ r r c £ r r r r £ c t t £
> k £ r £ c r r f £ r r i £ £ e £ t f r r £ C £ f t f £ f r r r r r £ T* c c r t £ c t r r t r c f r c f £ £ r £ t £ r r r f t t c £ t i
T> At A A f r t t f £ t c r : r £ f r r £ r f c £ f r r r r f r t £ £ t t £ r £ £ f r £ £ £ £ t f £ £ £ t £ £ t £ t £ £ t £
T»nr £ £ E £ t t t r r t r t t c r c f £ £ r t r r t t r r r t £> AT r £ t r F r r f f t r r r f c t r r r t c r r c r r f f t t . r AA e £ f r c r r r £ £ t r £ f c £ t f t f r r f £ C f f f t r r t f r AAAc e A t E t t r c t t t r f r t r r c r r t t t t r e r i t J r t t r c A £ f t t t £ t r r r f t r t r t r i r E r f £ r r f r r r r f r r f c r e r t r c e r e c r e r r e t t t r r r t i t c t r r e t t r i r
r c r r r r t e c e r t t t t e c t t c r r r c t t e t r i t t e r I r t r f c r c t t r t i r t r r t c r t c i r r t r r r e t r t r t
r r c r t c i t t r r c r r r c t i t e t t z i r c t i t e r i i t t r i t t t r c r e e r r t r c r r r t r r r - y y r t t i t i r
r r i c f t r r t r r r r r j t r t r t A A t r r f r r r r r i r i t r f C f r r t r r f r r r r r r r r f r r f
i f r TAX r f r x t r r r i f f r t r t r r x r t t r f f r x x r t r f t 1 X c c 1 t A A t l e r r c c c i e r t r r t t e r t r e r c e r t / t t r t i T f t c t f f A A f r c t r r c f f r r i r r x f c t c r r t t r t e t f x x r »
r t 1 . 11 r c r r t c r r r t t r t r f r t r r f f r f i t r r r r r r c f r rr x x t r e r r f x f r f r r £ t r t r c x r r r r x f f t r ■
r r c t t t r c a a c r
A A A A I A t
A A T A A A A
f f f f r f r t r rrr txt f t r rxfEcft rrrrrfcr i r r r r f f
   A  A A -y A A -.? lA A liT T iT ii .t .A A T»X, A C f t C ■-->» A C C £ A A t C C £ X t X f X t f f X tv > “» r-r AATx*^yjfiT/T' *> ■» "11. 1» 11». n f » !• irT /^ s j A A X A C'\> c c x - “ i r x c r x x x t x r f e x x x x x x x x i ; i : j { f f . ' i j t i f : r t f ; ;
. y A A A A A A A T’I tT A A A ^ riY/Ti t . t / f • Ti r» t.(» £ A A A A t £ £ X t f t X t C X X X X r X X X X X X X t f l l : l f i : f X r f » f ? f y f r fA ^T A A A A A A A A A A A t l . t l T . A AAT A T« A A A A A y \ r T t t t t t t T t t t t t t t T t t t t I t I t t . I f t f t t I i ! t T t t t I
T.trtiT T»r.T Tir.x»-AAE £ A- f c x f t t £ x x x x x x x x ( f f f x x x r * f x x f ; i t x : i : i : t ( ' ( f t t ' ' (A A A A A A A A A A A A A A A A /iT.T.T r . i . f ATOit^W AAC A A A A A A C X X £ X £ X X X X X X f X X X f X t X t X X . f Î t .* t { X f ! I ' : f ; ' I t S f t .*A A A A A A A A A A A ^ A A A A A A A A t.T I M .T .f A t t f X . t - J V «► X A £ t X X X X X X X X X X X X X X X t X C X X X X X t r X X I I ( X : X ' ' : : T T : X X I X ( :
T,T i.tx T .r XT f .x .x . f t f XC A £ r £ c X t £ X X X X X X X X X X X X X X X r X X r X X r X : t .- ! • r ' ; r X X X X X X X I X
gfTArAAAfAAAAVAXAAAXA AAAAAAAA A,Y< AXT» ittj OOfy y XI» AAAAC C£££C£CcrCrXtf£f£X£f££C£l £XfX£XCrXXXrxrXXX££XC£lÂAAAAAAAAA*/AAAAAAAArArAAf»trriAiTjTXT { • C y O f t . - U U f fO AAt ££££££££t ££t t £££X££t r£Xt XXX£XX£t t X( XXXXXXX£££t £èAAAAAAAAAAATAAAAAVAAAAtl.TruAjAjTJI, ti /.X-X I- I X» £• X C £ £ C £ £ £ £ C X X £ X £ £ £ £ C C £ £ £ £ X C X X C X X C c X X X X X X X t X £ X £ X X £ £AAA A AAA AAA AAAAAArAAAAATrTXTlAxA XIA • T.OX t»C a tj AAA£ ££££££££££££££££X£XX££££XX£rXXrXX£XXXXXXXXX££T££AAAA.AA AAA XAAAAAAAT, HAJTOtrC Xxl» X. i, AEAA C t £ £ £ £ £ C C t C X £ C £ X £ £ £ £ f X £ X £ X X X X a X X X X X X X f X X X X f £AA A A A A AAAA AA AATTAA tlTXTrutXTO t/ £/ A AAA A ££££££££££££££££££££XXXXXXXX A a fXXtXXXXtCXXfA AAA AA A AAA ATT AAA A V ' 11 VtTDTXKTJTD.ti XA, • t> Sir* A T> £ AA£ ££C£C££CCC££££££ ££££££££££ XX AAX XXXXXXXXt£X£££A AAAA A AAA A AAA ATiT>1<TrtXArCkn.TVf. -4 J»“> Ot.OOCfW T» »>T> £ £ t £ AT>££ £££££££££X£££££tr££X££rXX£XAA£xrXXXXXXX££XX£AAAA AAAA ATT*. AA T» » AA - -s» i. AAAA £ £ A%£ £££££££££££££££££££» ££££X£XX£r£XX[ X Xr£X££t££AAAAtAAAAA ATtn -rrn t,x *. —/ T>T»t»A £ A£A%tr £££££££££££££££££££ X X X f X f £ X X X f £ I £ X t X £ f X f X X £ £AAAAAAAAAAAAA Tmx. tyU AA C 1» T> £ T»£ ££££££££££ ££££££ X £ ££££ X X X X £ £ £ f f f £ f C £ £ £ f X X £ X £ £
AA AAAAAAAAA ATTITXtXTXt/ 1 / ................ NXTA £>•£>£> AT>AAT>T» T» £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ X £ £ £ X X £ £ - C X £ X £ £ t : £ £ ££CAAAAAAAAAAT» TTTrxXTrXfTTCnrA................... a AAAA AAAX A£ £ C £ £ £ £ £ £ £ £ £ £ £ X £ £ £ £ £ £ £ £ £ £ X f C £ X £ X AA f £ C X f X X X £ t £ X £ X £ £A A A A A A .A AATtTTTtTru rrC rX ftrrvrvO • N>T> A A A A a w a C £ C £ r C £ C £ C £ £ C C £ X £ £ C C £ £ £ C C C C X X C £ f X X X £ X £ X t £ £ £ X C X £ £ C'A A A A A A T . • T irm .TrcX trtrtnj.X vC — A A A A A A a • -v t w C £ C £ £ £ C £ C £ C C X £ C C C C £ C £ £ £ £ £ £ £ £ X X r \y £ £ X X X £ £ X X £ X £ £ £ £ £A A A A • • 'TTTkTTTTXkJTTrrrEfUTj - -.WSJSXAA ' AAAAA • A 'v - - A £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ A £ £ £ £ £ A £ X £ £ X X C A V X X X £ £ ( £ X £ £ £ £ X £ £
-A A A A AI -AO.XTA.Trc IXOCC • A A ^A A • • £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ ££ AT*£A£X£ X £ £ £ X AA— X £ X X £ £ £ £ £ £ £ £ £ £ £-AA TTOtXAC TTTTinrc ^ £ J ■ tA A A A A C -J-«rA £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ A£ A A£ X £ £ £ £ AAvJAAAr £ £ £ £ £ £ £ £ £ £ £ £ £
- -AAA t r x o T. -c Trr.i. ocvCrv— j • a a a a a •«- a a a a e e x c £ e e e e x r r r e e e r x a a a a a a e x x x £ AA — x t r x x £ x r c c x c c c■~rTU ti 111'l A VtXWmXjLviKC— t> A AA • • - A AA £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ ETAAAAC £ X £ £ AA— X f C i r C X t r C C X C E
■AAt, TTTTmXtvEvEJEjEjEfÙ t x .......................... £■ ...................A A £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ AAECECEAAA £ £ £ X £ £ £ £ X X £ X £ £ATrtnXATTTTrrtj£v£vOEjEj£j£j Lr-y ijZ tiJ \> A £ £ £ £ £ £ £ £ £ £ £ £ Z E E E E E E EAAAE £ £ £ E A A \, £ X £ X X £ £ X £ £ X C C £-AX»mx'J I |rn ri>£v£K>E»EjO£vt>d i f ■ yy ■ ■ ■ ■ £ A £ £ EE £ EE C EEE £ E CE £ E £ ££■ AACCEE E AA £ £ £ £ £ £ £ £ £ £ £ £ £ £ATTTXAAt, TO EvEv£vEv£>£»£jE>Lv£>£)>JAE................... A A AA \JE E E E E E E E C E E £ £ £ £ £ £ £ £ EE EAEC E£ AA £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £El AC ErEJE CJEJEjEJEJEJEAEJEJEACjE. -J\X\>E- • • A~~ •*. A E E E E E E E E E E E E E E - EEEEEE EE E EE E E^E AX E AAA E E E E £ X £ £ £ £ £ X £ E E
TXAXx •trc E»£>£>E>EJE>£>£>XjE»£>Ej«4«.»ErvrA • -4A -EVJ A E C E EA EE E EEE CA £ £ E £ £ E £ £ E E E E £ E £ £ E £ E A £ X £ E £ £ X £ £ £ £ £ X E £TrOtrCvXx xTTtXtvEvEvŒjEjŒ^AfjEJ -4-4 \EA — — r-J AAAEAAAAAAAE EEE A E E £ E E E E E E EE EE £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £trrXTi Œmxrmc&EvEvET-JEvŒiO -NJ-JSE».................. — -4 -4 — AAAAAAAAAA E E E E £ E £ £ E £ £ £ £ E £ E E £ E E £ X £ E £ £ £ E £ £ £ £ t £ £ £ £ £ £ £ E £■ojvTvxvtvxrxrtrc e>e>e> -4Ev£a4Xj-4 - -4 a a a — m a a a a a a a 'a e e e c c e e e e e e e e c c e e a e e e e e e c c c c x e c e x x c c e c c e e e e
O JVTTtrC UV£kA£j-4 - MNJ AA EA ' AAA -TAA AAAAAAAAAA AE r C E E E C E E E E E C E A £ E £ £ £ E E X £ £ £ £ £ E £ £ £ £ £ £ £ £ £ E E••£» .TmXvEvEiEvEvEJ • • Ex>*£J A E- A ' A ' -- "VA A A— AAA AAAAA AAEEEEEEE £ E£ £ EEE E A E £ £ £ £ £ E £ £ E £ £ £ £ £ r £ £ £ £ C £ E £ E £\J OJVTV XXjEjEvEJ • • ■N>-4-4V> • AA ' • — » • • -< A AAA AA AE E E E E E E E E CE E E E - £ £ £ £ £ £ £ E £ £ £ £ £ £ £ £ £ C £ £ E £ E E £ E £-«4 S>«4 -N> - - A A A A A A —4 ................................................. A A A A A A A A A A E E E E E E E E E E E E E £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £
• A • • AAAA A AAAAAAA • .r. - • —/ AAA A AAAAEEEE EE EEE £ £ E AE E E E £ X E £ E E X £ £ £ £ £ E £ C £ £ £ £ £ £ £ E £A A - -XAA A AAAAAAA AAAAAAA A Nl AE E C E E C E C E E £ E £ E £ £ E E E E C X C E £ C £ C C £ £ £ £ £ £ C £ £ £ E X £ £
AA AAA AAAAAAAAA • ■ AAAAA ' ' ' AAA -4 — AAAAAA AAE E E E E E £ E E £ £ £ £ £ E £ £ £ £ £ £ E £ £ E £ £ E C £ £ £ £ £ £ C £ £ E £ £ £ X £ £AAAA • AAAAAA AAAAA A A A A A ........................- 4-4-. A AAAA AAAA AAA AE E E E E E E EE £ EEE £ £ £ £ E E £ £ £ £ £ £ £ £ E X £ £ £ E £ £ £ £ E £ E £ X E £AA AAA - AAAAA AAA E A A ............................ -4-. AAAAAAAAAE AAAAE E E E E E E E E E E E E E E E E E E E £ X £ £ £ £ E X X £ C £ £ E E £ £ £ E E £ £ £ t £ £AA AAA • • • • AAAAA A A A ........................................ AAAAAAA ' AAAA AA E E E E E EEC "AE EEC EAA £ £ £ £ C C E X £ £ £ C £ £ £ £ £ £ £ £ £ £ £ £ £ ,
A AAAA ' • • AAAA AAA A ................... — -4 EAAAAAAAAAAAAAAAÆ E E EE AEA E E C E E E A £ E £ £ X C £ £ £ X X £ £ E £££ .:. X X £ X X £ £AAAAAAAA A ' ' AA ' AAAAA . . . A AAA • ' VAA - A A A AAE E E E A A » CEAAEEE E £ £ £ £ £ E £ £ E £ X E E E £ £ £ £ E E £ E £ E EAAAAAA AA ' ' A AA ............... A AAAAAA EE AA £ CA E £ £ EC £ E £ £ £ £ £ £ E X C £ C C X £ X £ £ X £ £ £ E £A AAA AAAA AA A - • A • "A-. — A A A A A A A EEEA A Æ EEEE EEE CEE£ £ £ £ £ £ £ £ E E £ £ E £ £ £ £ £ X £ £ £ £ E £
AAAAA AAAAA ..............................A • ' — AA AAAAAAAAAAE £ E E £ E E E £ E £ X E £ E £ £ £ £ £ E £ £ £ £ £ £ X £ E X £ E £ E EA A AAAA AAAAA . . . A A AA E EE E E E»AE£ E C £ E £ £ X £ £ £ E £ £ £ E £ £ £ £ £ E £ E £ E E £
A A A ..............................A A — - — . — • AAE EEE £ EE AA EEE E EE X £ £ £ £ £ £ E E E £ £ £ E £ £ £ E E E E EAAA • \4 AA E EEAE EEE E EE-AEEEEEE £ X X X X £ E E £ £ £ £ £ £ £ £ E £ £ £ £ E £ £AAA • AAA —. -4— 4-, A-WNJ AAA A E E EE E £ E £ E E E E E E E E C E EE £ £ E £ E £ £ £ £ E £ £ E £ E E £ £ E E EAAA - A • - AA AAA E E £ E £ E E E E E E E E E E E £ £ £ £ E E E £ E E £ E E £ £ £ E E £ £ E E E EAAA AA • • • £1 A - - . X J - A AA A AA E E E E E £ E E E C E E E E E E £ £ E £ £ E E £ E t E £ £ £ £ E £ £ £ E £ E E E EAAAAAAAA -4 — AA~» A A E E E E E E EEEEEE- £ E E E E E E £ E E £ E £ £ £ £ E £ E £ E E E E E E E EAAAAAAA ' ' ' A •— .T. • A Æ -*4 A A .EE E EE E EE EE E E EE EEEE E E E E E E £ E£ £ £ E E E E £ £ E £ E £ X E £AAAAAA AAA A A -4 — -4-4 EA AA AAA E E E £ E E E E E £ E E E E E E E E E X £ E E E E E E £ £ £ E £ £ £ E £ £ £ E £ E £AAAAAA - ' AA AAAAA AA-. - m A E A • • A A E E E E E E E E E E E E E E E E E E E E E£ EEE £ E £ £ £ £ £ £ £ £ £ £ X E E E E £AAAAAA A AAA • • • .T\£. • . . Tj-ft A E E E E E E C E E E E E E E E E E E E E E E £ EE £ £E £ £ £ £ £ £ £ £ £ £ £ £ £ £ £ £AAAAAAA A A A'A-J - - - -ET» A A • A E AAA A E E E E E E E EE EEE E E E E £ E E E £ £ £ £ £ £ £ £ CCCCECEC £ £ £ £ £ £ £ £AAAA AA • • AAA AA • AA A . . A AAAA ■ ' AAA ' A A E E E E E E E E E E E E E E E E E EE £ E £ £ £ E £ £ £ £ £ £ £ £ £ £ £ £ t £ £ £ E XAAA AAA AA • • ' A • - - AA AEAAA AAE E E E E E E E E E E E E E E E E E E XE E E X £ £ £ E £ £ t X E £ E X £ £ £ X X X £ £AA • -AAAAAAA A ' - A A - A AAAAA E E E E E E E E E E E E E E E E E E E E £ £ X £ £ £ E X £ £ £ ' ; : X £ £ X " X £ £A AAAAAAA AA A . . . 1» AAAA N» £ E E E E E E £ E E E £ E E £ E E £ E E £ £ E £ X £ £ £ £ £ E £ £ X X E X £ X . £ £
A AAAAA A . . A A AA AA AAA • C C £ C £ E E C C E C C E E £ E E £ C C £ £ C £ X £ £ £ C X r C £ £ £ E £ C C . - £ CA • AAAAA AA ' - AAAAAA . . . AA A AA 'M AC E £ E £ E £ E £ £ E £ E £ £ E E X £ £ £ £ X £ t £ X £ £ £ £ X £ £ £ £ : £ £ £ £
A A A AAAAA AA AAAAAAA -» -A • -4 . . . . AA • • -4AAC E £ £ E £ E E £ E X E E £ E £ £ £ E £ X E E X £ £ £ £ X £ X t £ £ £ X X £ £AAA AAAAAAAA AA AA A A A A "'J............... A 4—I AA \J ' • ATiE £ £ £ £ E £ £ E £ X £ X £ £ £ £ £ X E £ £ £ X £ £ £ £ £ £ £ X £ £ £ ; £ X £ £A AAAAAAAA • AAAAAA .................... —/ «AAAAAA • • A AE X * £ £ £ X £ £ £ C £ £ £ £ C £ E £ £ £ E £ £ £ £ £ X £ £ X £ £ £ £ £ £ £A AAAAAAAA A AAAAAAAAAAA • - AV - 4-. -4 • AAAA A-X\4 AAE £ t £ £ E £ £ E £ £ £ £ £ £ E £ £ £ X X £ E c £ X £ £ £ £ £ £ £ £ £ £ Af £ rAA AAAAAAAAAA AAAAA A A A A ................. -4-, — AAAA fc- AE £• AAAC £ £ £ E X £ E £ £ £ X £ X E E X £ X X £ £ £ X E X X X X £ £ £ £ £ £ X X £ £AAA AAAAAAAAAAAAA A A A ................... 4 -4 A AAAA ' • AE E EAAAE £ E E £ £ X X £ £ £ £ £ E £ £ £ f £ X £ X £ E £ £ £ £ £ f C £ £ £ £ £ A A t £ £A - AAAAAAAA A A .......................... A ...................AAAAAAEA ' C E EA A A £ E £ E £ X £ E £ E E £ E £ £ E X r X X X £ £ X E X X X X X t £ £ X A £ £A AAAAAA ' ' A A A ...................... ' -4-4 • ■ • AAAAAAE A ' AA E E AAX E t £ X £ £ £ £ E £ £ £ £ £ £ £ £ £ £ £ X £ X £ £ £ X £ £ X X £ £ £ £ AA X £A AAAAAAAA A A AAAE •NJ - • • • N4AA-4.rvxv • AAAE CAE AAT&EAE EE £ £ £ £ £ £ E £ E E £ £ £ £ X £ X £ E X £ £ X X t X e X X £ t X £ X X £ £ A X £ £ X £ XA EAAAAAAAAEEAAAAAAA£A£A . . AAw • • A E E fEA EE -X A EA C E r E E £ £ E £ £ £ E £ £ E £ E £ £ £ £ £ £ £ £ £ £ £ £ X £ £ E X X £ X E £ £ £ £ £ £ t £ -
• AAA ft AAA • AAAAAAAE AA • A AA AX E E E E A AE C £ E E ' £ X £ E £ E E £ C X £ X X £ £ £ £ £ f X X X £ C £ X X £ £ £ X £ X £ C X X X XAAAAAAAAAAAAAEE EEAA-AEEAAAAEA AAAAAAAA E E E E AAA-4 AAAAE £ £ £ £ AE £ £ X E £ £ E X £ X X £ £ £ £ £ X X £ £ X £ £ X X £ £ X X X X X X £ X X £ X
1 » AAAAAAAAA A EE EEEAE £ EAE E C£ • AAAAAAAAAA AtVC E AA £ £ £ £ £ £ £ £ £ £ £ E E £ £ t X £ £ E X X £ X X X £ £ £ X X £ X E X X E X £ X X X X £ X £ X X E AAAAT,AAAAAE £ £ E E EE E E E E E E E E E E E • AAAAAA • C A A E E E A £ A A t £ £ E £ £ £ X £ E £ £ X X £ X X t X r r : r X r t r X X £ X X £ X £ X X t X £ t £ X r X X r X X £ x A—AAAAAEAAEEAEE E £ E E XE CCCCE CCX AAAAAA E E £ E X E E £ E E £ £ E t C E £ X £ £ £ £ E £ £ £ £ £ X X t r x r X X X £ £ £ X r £ £ r E X £ X r X £ X X t f X X X t X X £A AAAAE £ AAE £ £ £ £ £ £ £ £ £ £ £ £ £ £ AAAAAAAAE ATVCECEEE E E £ £ Ct XE£ £ X £ X £ E £ £ X£ £ X XX f f r X £ X X £ XXXXXCXt A f C X C f t X t t X t XA AAAAA AA ££££££££££££££££ £ AA AAAAA E£EECECE££££££ECX£X£E£EX££X X X XI X t X X X XXXXXXXX XX X X t X t C X C tAA AAAA C AE- £ £ £ CAE £ E X EEEAE A XA CAAC C£EEE££ECC£Et££XXCXX£EEC£CCXT XXX XXXt XXXXXXt CC XXXXX£X£tX£t X AAAAAAA E E EAAAAE £ EAAAE EXECCCt X££CEEECC£CCEEECX£CCEE£X£EX£££E££CXfrrXX£XX X r X r X X T t X e t C t X X t X X C t C . X X t rAAAAAA A£ E AAC EEC AAAC £££££££ X£££EEEE£CEC££EE£CE££CE££EC££££C££CtXX££££rX££££££X£X£XXX££rXX£XXrXt£XAAAAAAAA £ A £ £ E £ C CWA EA CE- £ £ £ XA r££tEECCEE£CCEECXECtC£C£££E£C£E£££XtXXXX££X££X£X£X£XXX£££X£XXXXXXXXrxAAAAAAAAAC AE EXEEAA £ C£A A C £ £ EX XCCCCECECCEEEErEX£ECCC££E££EEC£££XX££X£££££££XX£XXXXXXrXXXXXXXXXI X X X X
A X AAA AAE X £ C E AAE £ C AAE XCECC CC£ E E E £ E E CE E E E r X£ Xt r XX r r XXX r XE T - r r T - » - « . p * . « . 44«- «-44P4»- 4-4^44. ^4444, 4- 4, , - - .
FIGURE 25. FINAL YELLOWSTONE PARK CLASSIFICATION MAPS E C T IO N S
70
■» •> T» n TTTtTt *r T *> ”>
T i c r c c c • . i t u u L t tM tO t t c t z t t r » r t i u u -f> e t e c c rvnrv in .x>of»x> t>x/ r c r c c t c r * > r » f .o -^c c c c c t r N > - . / > o c c c c r t t c i r n . r - -v a
r r f c r T* -C* j» o c t r c c r t " t. t>r f c t- !• f > r r f c c c f
»«rvi» r r t> i»c c r t c r c • •• T»f e e c t r r t c c* -af*int7ii*r»M »»i>c, r-c»
r c r e cT »c r r c £• '>c c r c r t c t r r ^ v »» n n r .
t t c r c e c r I e t T* m t r . c * i i iT /v n m » c r c r r c c e % • -^ u n r» * /* . •T/T///»»r/ï/T»c c e r c c r c n ^ T » r»»vivf» o o n i i t r i r r a »
v> r c c c c t r c t > iu«7> cid**c< cN/T> T>T> r t r c r r r r c tc i.
T>i>T»T»T»t» t t f f C C t* — •*• i>Ot> "> *»ï’ -vaT f r C C C ’• t* ■r r>r>*>r>T>r »>?»»>£ t r c r t C C r'J'» t. »• j v • »*»
( t T i T r r t ^ r v r \ f > ootj c(DO n tm t» c » o c^ C
1 •miiin^ooooottottc trim HT tritor>t»Uf>
l>IITn/T*T-C>(>'*(
r»T>T>T>t>T»r»i f*»»t rr c r r c C r- T»nT»T>rkf »**»T>r r»r f r- cT»c »> rnr»nrv/nn.tC1-* r c r c »>▼> tnr*>** i>»ra .r»nT*rxt»rnt«• p t r » ^ t r c c ^ c f c c o*nrikFx irf> fir«c»cf f c f»f f r c i>f» Wva // **WaC,C t» lrT‘tft‘1
r r c t f r r »>*»»> ' —a ** r - -« {—v a r ir in T .i> c * { .(*>«» c ^ r c e r r i c i »•«—c\> *> ^c - r —« ' i »m t i . <•»»%£ c f c r r r r r c * > — '•( r c r* c-vix> n m r*f- t•>»%f t r r r r r r r f f —« r r r r i M r ^ iT .n r « r n . •
-TT-M T1 P"T-T» T1T- %
f ( Vf < f I IM * ■,-a fkfVTvrkft.H
T* y> rvi» trxn ix i,t. st. yrtnjxj ■ f.rvtvfvfvr Ttrtkt»' fTTxtvnnif. T/Vï'iT*T-y:x»vim». -n-n •■*'»■»•»•> stvrvtxt' ■ 'r-yfr'> X tkf» TiTTT/-jrnjTtm.rrtn» fn
-r~r-> X -iT., *>T>ytyyr-rtry yx-jot»
■ r 'm 'm o ‘fr">'*rr, r f IMI ifToxi I if > • •ï'rT»c»crtTTnot>trrvc*x/rmT> tmr» • •
-y-T-> - ) f i Xf"ï x m TUI f IV TTTi • •xx'j'i*T*»T> xxcxtruTrfTfTrmxmTTTTTvL crrrt» •
•* rx T X * y ^ I .T |Ti£xrrir»t 11 i r u 11 *i ■ i >i ■ 11 l o i i u h t t ~r-rrr"r-x />niii’ici xtc, i/rfTr*TTnv{/Ti ii7ir>xm' •57T-.X 7 fJVfUU!»UIWXMtni7|ll£xCr»> XTTVCr
C- .«imit/xi TA» nrkftT r- ATlT»TTfTtiT»TmoCA/xv|>o t x t f v i-iruT-t/i*L ij\>
nri TU /c^o{•OX» (-X»X-OCxC/C>Xx
(/XxX—CV X/ fX. X» -a-X>J%> \mCNJ O U \)C c r c C'aVX>X>X>X»X» f c c c T» x»x»ot»x»xx crrrc
t>Oi> nXxX»Xf\XT»C TTCCT.xxntiif c r C r r r f>
c c e r r r c c c r r ccT»c rtrrrccrrrrx t*T>ticcrc c c r ©T> cccecT»
XX" - f TXTTAT-*
x.xxtxr. TAjX'TXXXX.1.\> X»X>T»ttttXAAAAAT» f» A»— lA- TTATT
x»x<--xv ■ \ j X.» X» x»x>x>x.xx-tNAra n i c C T » n>x*x X» XxXxXx • X/X» f » C C t r - NTO x>x»N» X/ xx • •& x»x» • • c c c r rswaUX'X»• • T> CCI» V - • cccf» x«x» tt-r'fic c- c rrccrx» Tf.rrATt>xiI X ................. - • r»>l>XCC • t XXrnDf, TAlXXtiTi
t Xx - T> CTVCCT>T>C7» - ~-»X»X>X/X t/tXX ">■i>x»x*x>x>xxx*x>ox*x» c -V T»Ticrrcc- te c% — t»xxx»x. mix •■> •XxX>X»XxX»X>X>C>XxX>X>OX»X>X>X>XX • Cf- • • • CC7> r- Xx t lA'^fXAT—r'Trym n jTf l'fA'H H It AU X<.Xx TITIII TTXA»XxXxXft»XxXxXxXxXxXxX»XxX»C'X»X*XxXx CCCC1» • T*C A • C -a FA. «T 'iAA
-y-TTT~j TTuxit;111>n .*> x r rm x x x rn x i 'n ' i t r r r n • xxXxXxXxXxx-xxx»XkX»x»xxXxf< - c t a jy i t a i ' ia a * » t »"I 'AX> x/'xMM.j.xjvnTma'i'ix. t m x» ttti x*xxtxX»Xxxxx>Xxx>x*t>x>x»XxXx'-rv • c^t» - c rtac- - xa.ia'ta tita"> -« •■> • TTX/’TDJ' T|fU(tl1* •.’> x o X A»XX>X>X>X>OOXxX>OX-CX CT> CCCf X. Xk" TxrVTTT. TTC TrcfTTAX»xxx/ft'ni:fTryrryyrt/T» x>x>rxxxX‘XxXxx»c»xxx*x>xt\>c» cctt — c c c r x» x> tttx. x/x*n n nxA/xfyTTTTTvx»x«x/T7Tr»T>.A.TOryaJmWAt>x*xxXKX»x>x-/*x»x»x»x»Xx-. rr r r r r r r Xk x»X. «AX-y^rTT T A x X ttr iH X t f JX'IXx TXXWXxCk(»XxX».Xx(xXxXxXx -V -, C C C»>T>r C C C C C XaXx•*> ArrATrï xrxtxrixnTT*TTrTtTTvoXkX»x»ikC>A>x»x»XkX»x»xx£xx»r- • xx crc rcrrrv x>xx TT rr-jr-vn iiiiiiiiii:x jiixxXKrwXkX>x>x>A>x>x>rxOXxx>xxoxx V TTC r c T»trccrT»\x
. . . . . . . . . . . . . . . . . . . . . . . . . . xroT T T f T v c » I M 11111' • • x r x x x r x i x x x x x > x x A > < x x > J> x x X > X fx > x x x x - « x - a t » c c c r c r c c r TTT» ixXkXxtiTi'i'i: TTurrc xxxxxxXkOo x»xxx>xx --x errer rrTT . . xxXi xrt»x»xxtk£) TTTI A "xfxxxrt, xxX>xxXkCx-w -«x«-xx v—x ■ crrr t&rr x»TTT» . XXnfixxxxxixxT» TTTI '~jAmjtrtxTTtvtn*xxXxXxXx-v*. -atA-XxXxXxXx r cr»>oT>tr^T» xAxt»stit. -m TtTruTTTi irt»XxXkC>x*xxxxX»xx— c x»x»-*xxx» T>T»crrcT»T>T»cr xxxxx t»T» . . x/xxTT -tttxi j ff If mi I X» XXX, xxXkXxXxX»fxXxXx--k'»xxXi I» x> f» r rrrrrcrrc x»xx
r»f»x»x>TiiJi.»x»(-r» t» t.xxTiTiI« T»TT»|X»X»<»
(>r»X>i> Tfi/r»tfX iTrtx i/Xx TPtAAAAiT» UT iniXiTAiT.X XX
.XXTXTTt» TTIiTAIT.X* I»T> f TJT»X. Ix(. Xrt» XxX'XAlTA T T» TAXxXX'X7A*X» XAiTIXltAïUT' XiXXTXXxX»! TAXXxX'XXlT; -■> XArtXl» Tinux.x. IIX t.XxXX» • Tkt» TTT A. IjTlTA X* Xktt» T* t.X»XxXxX. T\X» X' XjT» TiT'T» T» j T»|it. 1. XX»X*X/ IxTTT tttiTit/xxïjt. TiiAxXXT- ITvx axttuxjT/t|ttt ixxT» a *»T iTn a rr» x xititaxtu»»T.A TAJX»T»'4 TJTA t TiTTT» IfTTXlTlIxTtXX (tiriT» TTXArt TTtxrrjAxAi xix t» rniTiTiTiTTjifTvux
TlXf-X\kXxXxXxX» Xx-vaXxX-X» -afxXxXxXx r C C r r c C C r r r t>X»X»tt*> X»Xx T»XxT<XAA,. ATiTIXxTtTTXxXxX, TxTT»» XAXXAXTI-' XlTMXkXi— XxXxXxXxXx-xXxXxXxXxXxXx XxXxX» r C C C r t r C r r r>Xxt» ATVXxXA*XxX*X«tt»A . tXJÎiTTTTTiXATTXrrXxTTT» r>XrXiT»TTXiX ( . ( . (X • • xxX»-. f»xxA» Xx r r r c r c r r c f - xxXxX>xxx»xA/Titit«>TA. ac/ttti tttix/t? rxxxrxrxcxz xxI XxX, X«TTTT7> XxXxX, TttJ—a • • • (.fxXx--x t» Xx CCrCrtCC T» £• XxX-XxXxXxXXTAAI1x"i TXT TTTTTTTTT.txT* tlTTTxTfX»XJTlT.Xx{ •X»tXxXjXAAxTTTTTXxXxXxXxX, • . -a-.,X/ -*t« C C C C C C C rt»»»\xX• ATvXxi-txXxX, TitiTi t tiTTTfATTT» TTT* TIXAAxTiX T— XAA/TT'Ï XxXxOXxXxXxXxXx Otx X, »» CrrCCCCr t» I AT\x»t./>*Xk»A>Xrtf A-> ttjiTTTTTtta/AT, T«f*XJTT»»TTT»T TxxXAxXkXi xxXxXxXx NX • xxXkt» r C C C rr rrc- TixxXxx xxAti~a • r'T'n rrs XxX.XroNX -X/T.TtT T'Axa, Xx • -x-x T, XJ f ru A f IX, . . .X, XAAfXxXAAxXkXxXx-a • •
T n r v t , TOxXkX».................
xrtn/LUj o -*v x v t»TkX/TVX>XxX>XxX>-X> Xx T TmXxXxXxXxXxXxXxXxXxXx Xx "vr»T» • - •TTTnTTTXxXxXxXAmXxXxXxXxX» • T>. - ttttttTvxxX A A xXxXxXxXxXxXx -a T»%.• - tttttvx.XxX» XAtrrrix*£xX> • r i > ' • •
-V .n \rocT>T> r'Nx • N> x> stvr» r r c r r \x x»xx■ TTxj» rcrrcT» x/aaxxx, xxx» x»'jv x f «r» r c r r t» T r rx r xiii>x>X>x>u -aXr-UVtW* c C e r T > .ta/TTTXAxXxXxXxXx XxXx
xuvTVTvnxx r c r r t»t> t/ t • x - x, -w x»x,x,• X. • xxXx • • T» ^ ...... s/LTx/xn • e r r e • • xxxx» • x» x/x,TTT* -a— NX • • TTC»........ \Atkt» NIC c c r r XAAA X »•t Nl i»T*TT - T»'Xx st». r r c r r t, oTrtjTTTx NnTT>T*T>-&T>r« eT>T>TM> • vTVt* CC C C TT ' -T trtMJ X»X'l’ITA/Ti Nrr>T>nT»Tyr»T> »T>T>toT> • • -At» • TkCT» X TVTA. X»•TfT> X X. XJT* N>T>T>T»T> T> c CWCNI—j-x X» l i- C C* NX AT. TAAA TA*
iTi x /x , /M l» —« ' T» - e t » *N>-a • • r r c T v r • T m T /n x j t a a a a ,AAATT '■» JI/MI» T» c T/N) . CCC T, TAAfT TA.I AT)Mil /ii'firii/ntAx............ N) Xx r r n» xxX/ta- t, t a ./. T»r»xT» TTA Xx Xx T» • • T>T> NX -a A r X» TAA' T- T»TTTTTTTTT» X/X/XA/TTX/A • CT* f- Xx-» A p TA/A Xx T/T»TAt»TUTIl/TTX«A*yA?> ....... T/TNT- • XxXxXA/AT»-/ CCC CNkXX TA, AT» • TiTi •A A AAAAA T- XxXxXxXx • • • r C C f- - T/Tx i A»• -AAAAAAA If A C C* ' ' ' XxXxXx T, C f, T» A (...... A ATT:/A AAAC r A XX AA T* • • T/A X NXTfTtA x m Xx Nl A TV - T/A AIT' N, XxX» Xx -XT» 'AimTor» • TT r Txr- a • ■ -aa/ti • n> t/n w « • —,'A TT -AT» ,r. A/ • AT.A r- AA/r, V TT ATV•AN TTAA Xx • AA T» T/TTC..........A TT - - p- N» T»T»T»AA T* -a - AT XxX» • • • T*r T*txXxXkXxXxX,
X/XlAATTT»
T, T/TTT» f AAT. TjT/TAfTiT. TlATVX. IlAA tiA TTTTT»X/AAA TlT»
TTTri/TITTr»
I.X T*X/TJt»T/
lITTTfATlTjT ITTA TlX/MMT|Vf«ITTT»* «» AIPUTf AATTV» TlT
A attx.x/aattat/x»
.ffAAAAA TTTTTTAT a atIT/AAAT» xn/TITiTTATITtA-. AT* -AATITV/.X, TTT* f»A-|• ATT A A A AT» X» Xrt , AT / ATT A î r A AAAAAMM X T» TlIlT'AI, AT/AAT TTT» A: Al.
ATTTXxIVXxXx •Xx ».ri.ffTTTTT\x*x»x, . C r C r c f r» -x-aXxX/Xrt. TTTTXxXxXxC Nl ACCACr AC- X»XkX»X»X»X, ATTmxxX—x ■ TtCCC-A I. xxXxxxx, Xx T* AArr r-ANjNx— xxx»x,x»x» Tf/Mx r- r- r
r> TT XxXxXxXxXxX'X» AX.X» -» NT*.*T» -rX.X'XxX./xXxX» TTT* (» X—»—»-»x»Xxc- {•«•XxtxxxxxX.x/TTfrriT* n» i . : —j hx>
nTTTTATA n/Tt*TTTTATTTTTTTrri »
-«-• f • : » AI ■ f » ATT t ,Ti I •
FIGURE 2 1 . FINAL YELLOWSTONE PARK CLASSIFICATION MAPSECTION 11
71■vMTna» i> r T»r-
•»» n » f I
ryrt trtTrr» *1 rm TTTT» •n Tt t i-.TrnTrriTT
■>■»*>•» T.TT TT
TT “1 T TT»f 11' VijTTT> t«T>T>T>T>TTT>
ttt>tt\ , ^ ^ f «f f «O f ff f '/yT>T»V> (>/•/>{< f
V» »• f.<» utittotitiin im tr■ \y in i T i i i m . rrr, ( j i t l t i r f n n m u t i
»• r ynrtiif imt. n ntnnntn»• »• iiTnrr- r irr/rfTtJ ynruin.
i» f T /-T onnrrr< T n/T rf> tn jT /m uT r»T/w ï»'»'r utM’vnnnnjxnn/ixirtnnrtrtiyrr>fn
\rvT > 6 y>tjtit>ijt‘ini'UTruyftfifjfirTfinnnnrtrtnnnn
lO fx.
OOl^Of T<T.//T»T. LiCrlfl
t. o tttnnnnrtitftrm nnnrtnrtnftniw t. iti.’ rytnntrrtrjnru'tnfTnnftnnjVTrtrti'tnrtnn/^
•»T>T»CT» T»T> t ’U-r T»TTT»r r *>T» n«
n;tt r»T» rt> r 'r ce c r » r
*»TT>C c T»T>T» r>T>T> VT»TTT&FT»T,T»T» CT» •
t T>’>T>T»»>T»r»T*T»T> t»t»T»t»T>T»1*T*T>T»WT> -VT»T»T»T»T»T»^T»%%T»\,T»T»T*R,TT**T»T»%^^W • r T»»»r T>T»t>T>T*
TTT»T»ri* T»% w TT»r tT»T»T»
t~y'j'rr> ou ut>j t rT>T» ■> y > r r tn tr \u ~ ^ -gT» c Nj T - jx "ro, U \ r o v t\f T» 'X'yUlfy LTV'rer T>T> VT» \ '
' i ' r u u u o . t r o ^SJ tf~r't'tfr\U-0£>.m>U
fTfTT TTfT-f X/r\t>UC*mj-J\i \> T* T. T - jr - n r lr 'j .xJ\r> TTTvc» T» n; t»~j ,rr> TTTf»-
r — 'TUrrfM *T» cTr>JT> rrry y y ^■xrrt Tl N * c r t t c r ^ T >
TfTTxrumfUUUUtfUU
■wt r rc-rmv T> CCtT»t>T>
'mnnrtrmrtrtruwnfjnfirtt « » itiiit r ■> t nmfxjxnnrtrjfirtnfTrmftronnj t/r^uo ouuc t
T/TTi»r T iT fT rtro n frr/T iT /T rir£ rriT n rjT n rT /v rrr» i» in rr» .c ,t,£ /t*< » f# t»« » î.m .c .f.T u/o liT/vx» T*rKrTTnrrt;xrtrT/Tmx<7/TnjT«'rnr»» t-uuuuo u u u ouuuu u~t^
ot>u rnrr t> ■oyiyiyrjnrtnnnnnnnnnnr^uuuuuuuuuuut>uuL ucOC truyniT, tm tnnnnti tnnrt/rrr yr^yooottooooooooot. oooc
\f ttin. u yruxr uyiynnnnrm i im ii ouuuouuuuuuuuc uooucimyrx. ->i y>oot>u y-ouvxrtnnnjyrwrrrTuuui^uuuuuo uuouuc ouuttiTirifi-j-T -nt.uo utitrt uufTtiirrnfxrru*t>t,out‘UOUO'jUUOUi> ot.uuot. ou oooc
• ou ou fi u t irtj"’yoouoouot»ouo(,i»ouu titt0 t ‘u o u f 0 0 ouoo">*5 Tl C uutrtye. ti'u^TrTtrt>oouuuouuuooouoouwuTr*u^ouuotiuououoL
t. tr "> T in tt UUt/ty ' UOUUOOUOUOOUUUUOOttOOUO UOU ' •uoooooctfUU c m> X> u ItUUUUU OOUOUOUUOOOOOUOt^OOUOOUt. f’ u oooooooc
r TjT. ■xfm jnuuouuouuooouuitouoooouoouuuooooouotrffuuo ^>**uoooooocikr> ym -T~rrr\ouoouuuouuooooouooouoooouuoooouc ^nn>tujoo*>oooo-oooc
u irv"*'y'i"’tTtyTr\uooooooouoc»t‘Ouooouuuuoououuoo-uin>‘tiw ooooooooootfO O oc »m ty<s^uuuuoi^mtjjitut,uuttOuux,uuuuuuuuL,trtnmyrou^.tu,ujjjjr,umj^ f ^ *r*r*r*T*> ■'Ty\ôcj-ouoooot»ottoot‘UUOUuoooooouooot/tTvtfXJxn»ooooooooooooi
'y-r~T~T'r~> 'n'rrxooooouuouooouot'uuuoom ^oooouout. irx/w t»ooouooooooooocTl'.iT» UOCfUOOOOttOUiUjUUOUOOOUOUOOOUUutJtt'UtnrUUt, uOOOUC ootr^ Till ir\OOUOOOOUUOUUttUUOUUU/>OOOOOUOOtrtrUVUXn ttt/t\oOOOUOOO£r^ ^\f\M i\uoouoooououuoui‘C oouuottot. uOt‘Ojjyn/m/vtnixr^\oououcu.
~t-> T'x't'ry*T> "y"*"*?» •■>
TD J* .n'y'fyyn~>-» 'r 'tyTu 'rt-i •j'wfyy'i
t>t>t> tt't uuooou-Jsr\>e e T»t>T» fT»T» ri T l Tl uuou-u-u-j'^T\ic
T>T»I»T»T»©T» U O U U ttO T / \ n TT11»T»T» %T» u \» •*»*>"> *y*^T*VT/t<*iT)*> • 'T r 'x rr ’ïT ' ix * • x/T»
I y>CAOoooouuuouuouut‘OOOue-uUuoouoinrur^tnn3tiJ> ooouououc ^>jjoouoooooouuttuouoi'UuuooouuuoiTuruyuT\t\jrit,m.. lutooooc itOOOUUUOUUOUUUOOOi‘OOOUOOUO-OOOU xn» .r\AT OOtfOUOOOmf’U
ouL r X‘UUtJuuuoC'U u o u ouoooooouuu ri.mi u uuooouuuoc rvr« X ot-uouu o.'»out^^oinnr rwi <>c o ououoc v.
*»t. it Siuouuuoou ~\'yT\j\t>t.,ouoouC‘OtH.'-u tToirT*» x ir r tiT /w T* uc x i» OOUOUU ~t~ in rv jii .c r* oo^L
■> v u OO-uC uuuuXIX ’*> XIX UUOl>UU-»UUUO
• » , -u u L' t>t> XI -w fvm vciiT ilt»T*xi T» f XlX» ou
nm> T*i» c-TT Tl uuuoUOifU 'JT»T» T>WV>»TVnTlX/Xl UUUU ■
ttt\c>C» T»T»1x r% % TTTIX UUUUUOU T»*I»»V BT» XXiX OU
T\c«ci r w rw »x iftrot‘0 T»T»7»*^ v u u
u t’ e e et»'vr>v^r\r\3\T\iOu x»XtT»T> t»
T»T»VT*T>f/T>t»^T»Ty
♦1T»T>T)T»T»T»\fT»T»*^T»T» r»f'O'&T»
XIX T*C f 1»T« ( , XIT»XlT, 7» f T> -.f»T»i»T> Z W X 1 -y -y iT , m i x 4*00 u t>
TlT» i»c- ct •’* V ■ i/xr*r*»*i ottuouu^ ninjn>-tW'oX Xi t» T»T» r X •XXX»ii<»X>X> O ' ~ t w \T J \>
T l ivc^s, Tsfi. ou utTz>u ooi^o OU —, x j\r> jtfxi r c T » T , T» yy^^uuuoouVTixi c r TxccT» ccT»T» N* t’t>uu-ooux' *«m e x r u x , x
v n r o u t>t* r r c r x * • uu•mnftro t» x x c c c c f • * ■ 'jrux ix • f * ticec % Cl O-Ctwifu ■x ix m Xi r » T&r f - -~tuooou x ix ix , £•xrt. o u c c c r c r x v w y » » -xAX i - ^ m ix c r i»xrt>x»£»x^«, t t e e r c w a ix » T » T f i> - - v r \ iT l C iC • T&f f c f T» -•» X NJNJV N> T»OU c c r v i » W » T> vf> - , sTTXXrXX T» \>
r e e - , uo • • - x x ix , r ft t c c r c t rT>WN> t » c x i- , j m x c x in
• c f x » r f f x»T»T*v oitUOuo x m x7» z f c r f w > p p T » ojtoo ■ x x ix r x t* cT ic f c CCC W » 0 ^ 1 -, XX. TIXI ITS, T»\>
t m c c c e c c c m y c * x>xsx - iv m , • ct*t> c t t vCT* f f C C C T*T3 • 0 t*0- ■ XIX x r t i - f c T»1» o
UCT*T»CCC CCT»T*^ troou X, X/T, XIX, • s i C CC —c n ^ c c c c c T * i l » X mciXix,x>x,xixixix*XkevT» r t i c c T i 'T>T*T»Cf c t CtXSM> -OOOOil TTxrtTti XlXIXl NrsXiC C C C C ! x t »
T»Tie CCCCTTTTS» X XI X lX lxm t/X X» • C C C t c x s ,
s fm xxx /T /T * o-x^xi-, .m \x *x i x ix ix ix > x *x r0 'x x /x ix x ootu’/ ’oot’ooooooooc Xfoooooo T l -«xiXkXiXi—, x r t i •"y~Toooirffnrot»oo{>ooe. txt t»um’ o o u o o o o o o o t r x x m x n o o o o o o o o o o o o o c o u .t>
vt*oooo xxxxiXTm£><>xix>Xi<>x><ii/v -tX'X'XiX. in iT ix /to x xNixi s j O Tl ■~j'r'j-T'y'yy\ooooo \ f v \if .x ,x ix » x ix i t i x r x
» - f S , vl» • X XTl -»-yXXXXX»£>XiX»ti SJSJC "W - f — x/x XX.ITXXex> o x x x r x xTTTi ^ x r x x x x £ > /,t i \ r s . c r
SXSl xruXTXXXrXXXrX -XXTTTI *y-jrX-»XXrXTi N» £ c C C S.
XXXXXXXX XXX fVIMix x x x x - i x x X vfvft.»\rvn
XXXXXXXX rvrv.T'.rvrvrvTvfi
** - , l i f r — VSTs- , - , t ’C t’0 ^’~J\J\JV
-,£>£i£,£iCi£Arsr^ IIX/T\£.£—
»• £» ti£*£,xrvsicXX. £ (>£,f—./vrs.X £ - , T £*£—/S/S/SJ
< • C— ivofi < T-TsTilS/s; X*^.£--.^,t>AiC»t,-. SJSi
/•£ .X i£> -^£ ,£ i£> £ /S f\n /S . t 'OOOU-^‘OUC w (>C.Ai£a£i S i i —fVSI/iC iU S/S, V — - , V i£
t^ ‘ ’tivt>oœ ££.£.£JV £«£>tif«£st>c> V
£>£-(.*-.£, £>£-£m rv£>£. s.£.£—,— £>£»£ £i£i£&£. —,- . -,£>£•£.• XSC><>£/T1Xmw
xrsftitrtv»» V-~£niT ixrxrirtr* icn, s. /"-, Yixmirtrcftrti u SI T/veitrc>£ft. -I—,
-,£• X ViUXri/T»£ Xi£—fs,SI £. i^^iX’inun
t’U t’UL OU
C CCXT» TTT»/>£>£i£lt/XrXtiCiCCC 7»Tt XITTtI TTTI %/TTTl SCSI •
x » c c C TlT* xrr, £*înc/*ri/T»T»T»»T»T»f xrrnrD’trtfxnjru e t»
XXT>T*t»T»C -,£» X/TTTTrftlX/T/TXx, s i CTlT*SI TlT» f XT* n ./m x /x iT m x i
T>» X X X f i n X cXTSXXX X X •
X X X C X X X X X X - /S )X l»c- XT» X Tfs» XT* xrsj»T* t c T*X • • M X X X ' TTSrsi SIX X X C C X X X XI - X •
CX T *X CX T *W T *X S> ................T*xc rXCCCXCCXTTTsi N/SISI Ox c e c c c c c e - T * W T * \ f \n x ^
c c c c c e c x x e c x x s n x js i c c CTIXC X c x X 'SI •
X X X T»XC f c x x X X -rv -T X X X X X X X X C T *X X X T *X X M
XT X X X X X X 1 X X X X X X X X X X X T X X X IX X X Xx x x x x x x x x x x x x x x x x x x x x x x x x x
• X T ir m x x x x x x x x x x x x x x x x x x x x x x x x x x xXTITIT/XXXXXXX XXXXXXXXXXXXXXXT/XX-X .rvX X XXXXXXXXXXXXXXXXXXXX t t x X X
XITfXXXXXXXXXXXXX XXXXXXXX TlXXTTTl T» XUTXiXXXXXXXXXXX IXXXXXXXXX7, XX TTTI T» X XXXXiTTXXXXXXXXXXXXXXXXTVnxX TTTTTl
TTXXXX T T X X X X X X X X X X X X X X X X T »X X X -T » t1 XXX X X X X X X x x x x x x x x x x x x
XXXTX XXXXXXX X XXXXXXXXXXX X XX XXXXXXXXXXXXXXXXXXXXXXXXX X X
x x x x x x x x x x x x x x x x x x x x x x x x x xXXXXXXXXXXXXXXXXXXXXXXXXXXX
x x x x x x x x x x x x x x x x x x x x x x x x x x -XXXXXXXXX XXXXXSTl
XXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXX- m -m -
XXX XXXXXXXXXXXXXXXXX TTTTXXXXXXXXXXX-tittx-T» XX x x x x r m x x x x x x x x x x x x x T T x s T - n
X /X X X X X X X X *
X XXT*T»1»»T»T*XT*%f » » T * •
FIGURE 2 8 . FINAL YELLOWSTONE PARK CLASSIFICATION MAPSECTION 12
CHAPTER V
CONCLUSIONS
F e a tu re e x t r a c t io n can be in te r p r e te d as being an e x te n s io n to
photography. Photography i s capab le o f p re se n tin g p a t te rn s in c o lo rs
o r v a r io u s shad ings fo r in te r p r e ta t io n by an o b se rv e r , bu t o f te n enough
th e re a re some f e a tu r e s which appear s im i la r , bu t a re n o t , and v ic e
v e r s a . Computer f e a tu r e e x t r a c t io n adds th e c a p a b i l i ty to d is t in g u is h
s u b t le d if f e r e n c e s in m u lt ip le d i g i t a l d a ta images and to make a d e c is io n
concern ing th e s im i la r i ty o f th o se f e a tu r e s in q u e s tio n . This e x te n s io n
can be e x p lo ite d to i t s f u l l e s t l i m i t s , in some c a s e s , when a d a ta bank
can be used f o r a c tu a l i d e n t i f i c a t i o n o f th e f e a tu r e s .
The purpose o f t h i s work was to dem onstra te th e c a p a b i l i ty of
e x t r a c t in g f e a tu r e s from d i g i t a l d a ta images w ith o u t in v o lv in g an
o b se rv e r in th e d a ta p ro c e ss in g loop and to compress unmanageable
amounts o f d a ta in to manageable and u s e fu l in fo rm a tio n . An o b se rv e r
would s t i l l be needed to i n t e r p r e t th e r e s u l t s .
The su ccess of th e d a ta com pression i s s ig n i f i c a n t in th a t 12
channels of d a ta were com pressed in to 1 and th a t 200,022 re s o lu t io n
e lem ents were reduced to a maximum of 45 d i s t i n c t c a te g o r ie s .
The com puter programs p re se n te d in t h i s work were p u rpose ly
developed to be as g e n e ra l as p o s s ib le , and th e u lt im a te su ccess o f
72
73
th e se computer program s f o r in fo rm a tio n e x t r a c t io n can on ly be
determ ined when th e program s a re t a i l o r e d and a p p lie d to so lv in g a
s p e c i f i c u se r o r u s e r ag e n c y 's n eed s . The p re s e n t u t i l i z a t i o n o f th e se
program s fo r f e a tu r e su rv e y in g , such as th e v e g e ta t io n and g e o lo g ic a l
c a te g o r iz a t io n s p re se n te d in th e t e x t , can be in te r p r e te d as be ing
s u c c e s s fu l s in c e th e com parison o f r e s u l t s w ith th o se p re v io u s ly
p u b lish e d in th e l i s t o f re fe re n c e s appears v ery fa v o ra b le .
The two keys to su ccess in u s in g th e u n su p erv ised fe a tu re
e x t r a c t io n program a re th e p ro d u c tio n o f a boundary map which c le a n ly
s e p a ra te s homogeneous a re a s belo n g in g to d i f f e r e n t f e a tu r e s and th e
ch o ice o f th e d e c is io n r u le fo r s p e c t r a l ly m erging s im i la r f e a tu r e s .
The over abundance o f b o u n d arie s in th e Y ellow stone d a ta in d ic a te s
th e need fo r improvement in th e m a th em atica l d e f in i t i o n o f a boundary o r
a t l e a s t a means f o r im proving th e th re sh o ld u s in g th e p re se n t boundary
d e f in i t i o n . I f r e p e t i t i v e coverage were a v a i la b le fo r a p a r t i c u la r t e s t
s i t e , th e optimum th re s h o ld fo r a boundary d e c is io n cou ld p robab ly be
de term ined . O th erw ise , th e e x p e rien ce gained from w orking w ith o th e r
ty p e s o f d a ta s e t s o r from p e ru s in g th e l i t e r a t u r e would have to p rov id e
th e im petus fo r d e te rm in in g a b e t t e r m athem atical d e f in i t i o n o f a
boundary. The two m ost im p o rtan t p ro p e r t ie s th a t need to be ta k en in to
c o n s id e ra tio n f o r t h i s d e f in i t i o n a re most p robab ly th e r e s o lu t io n and
some m easure o f roughness in th e p i c t o r i a l scene o f th e d i g i t a l d a ta
im age.
The use o f a p x p a r ra y fo r o b ta in in g i n i t i a l c l u s t e r s t a t i s t i c s
in a homogeneous a re a may have an advantage over th e manual s e le c t io n of
t r a in in g a re a s in th a t th e c l u s t e r a re a s can have a f a i r l y a r b i t r a r y
74
shape r a th e r th an be ing r e c ta n g u la r and th e d a ta s e le c te d from th e se
a re a s does n o t c o n ta in unusual d a ta p o in ts w hich could b ia s th e s t a t i s t i c a l
c a lc u la t io n s . The u se o f th e p x p a r ra y does have th e d e f in i t e
advantage th a t i t i s f a s t e r th an m anually s e le c t in g th e c o o rd in a te s of
th e t r a in in g a re a and e n te r in g th e se c o o rd in a te s in to th e com puter.
The use o f an e l l i p t i c a l d e c is io n r u le f o r merging and c l a s s i f i
c a t io n appears to be very a c c e p ta b le as ev idenced by th e f a c t th a t
p r a c t i c a l ly a l l o f th e r e s o lu t io n elem ents used fo r c a lc u la t in g th e
s t a t i s t i c s o f a f e a tu r e a re c l a s s i f i e d as be long ing to th a t f e a tu r e .
This f a c t i s even e v id e n t when s e v e ra l i n i t i a l c lu s te r s have been
merged to g e th e r to form a f i n a l c l a s s . A d d itio n a l su p p o rtin g ev idence
to t h i s co n c lu sio n i s th a t the i n i t i a l c l u s t e r s s e le c te d on th e second
pass th rough th e d a ta d id no t merge w ith any o f th e f i n a l c la s s e s
o b ta in ed from th e f i r s t pass through th e d a ta , and an alm ost u n n o tic e a b le
amount o f r e s o lu t io n elem ents had t h e i r o r ig in a l c l a s s i f i c a t i o n changed.
Most of th e e r r o r in c l a s s i f i c a t i o n occurs n e a r boundaries and n e a r th e
edges o f th e scan l i n e s . The f i r s t type o f e r r o r i s p robab ly due to th e
d a ta changing from one f e a tu re to an o th e r in th e v i c in i t y of a boundary
and in th e p ro cess p a ss in g through a d e c is io n re g io n of a t h i r d d i f f e r e n t
f e a tu r e . The m is c la s s i f ic a t io n n ea r th e edge of th e d a ta i s due to an
o p t i c a l e f f e c t c a l le d scan ang le e r r o r . The ang le a t which th e ground
scene i s viewed a t th e edge of a scan i s u s u a lly 30 to 40 d eg rees o f f
from th e lo c a l v e r t i c a l and, as a consequence, th e s ig n a l th a t i s
reco rd ed by th e sen so r r e f l e c t s an an g u la r dependence. I t i s re a so n a b le
to assume, how ever, t h a t th e u se o f an e l l i p t i c a l d e c is io n r u le could
ta k e in to accoun t th e an g u la r dependence. The an g u la r e f f e c t shou ld be
75
approx im ate ly l i n e a r dependent f o r th e d i f f e r e n t channels o f d a ta and
t h i s would amount to a le n g th s t r e tc h in g of th e p r in c ip a l axes o f th e
c l a s s i f i c a t i o n e l l i p s e s . I t i s apparen t th a t th e c l a s s i f i c a t i o n maps
p robab ly c o n ta in more d e ta i le d in fo rm atio n th an i s a c tu a l ly d e s ir e d . The
amount o f d e ta i le d in fo rm atio n p re se n t can be f u r th e r compressed by
v is u a l i n t e r p r e ta t io n and m anually merging th e d e s ire d f e a tu re s by
changing th e symbol o u tp u t on th e c l a s s i f i c a t i o n map.
When th e f e a tu r e s a re m anually m erged, c au tio n must be e x e rc ise d
in in te r p r e t in g a g iven f e a tu r e e x tra c te d from th e d a ta . For exam ple,
th e re a re s e v e ra l f e a tu r e s which re p re s e n t soy , co rn , and a m ix tu re of
corn and soy. A lthough th e re i s a te m p ta tio n to a t ta c h a s im ple
d e s c r ip t io n th a t i s commonly u sed , th e d e s c r ip t io n may be incom plete
w ith re s p e c t to th e in fo rm a tio n p re se n te d by th e d a ta and a lo g ic a l
manual m erging may n o t be p o s s ib le . D e ta ile d ground t r u t h would be
needed to p ro v id e th e q u a l i f ic a t io n s and a d je c t iv e s fo r a com plete
d e s c r ip t io n . For t h i s rea so n , i t may be im portan t to perform th e d a ta
a n a ly s is p r io r to p re ju d g in g th e in fo rm a tio n co n ten t o f th e d a ta r a th e r
th an u s in g th e ground t r u t h to a s s i s t in th e a n a ly s is of th e d a ta .
F in a l ly , i t m ust be em phasized th a t th e development o f th e
unsuperv ised f e a tu r e e x tra c t io n computer programs was d ir e c te d toward
o b ta in in g a com puter lo g ic th a t could e x t r a c t in fo rm a tio n from rem otely
sensed d a ta w ith a m oderate degree o f su c c e s s , which meant th a t computer
runn ing tim e n e c e s s a r i ly took a back s e a t . S ince th e developm ent work
has been com pleted , e f f o r t s can now be d ir e c te d toward o p tim iz in g th e
computer tim e and e f f ic ie n c y of th e program s.
BIBLIOGRAPHY
1. Lueder, D. R, A e r ia l P ho tog raph ic I n t e r p r e t a t i o n . New York:McGraw H i l l Book Company, I n c . , 1959.
2. Thompson, M. M. (E d i to r ) . Manual o f Photogram m etry. F a l l s Church,V irg in ia : American S o c ie ty of Photogram m etry, 1966.
3. Jen sen , N. O p tic a l and P ho tog raph ic R econnaissance System s.New York: John W iley and Sons, I n c . , 1968.
4 . Detchmendy, D. M., and P ace , W. H. "A Model fo r S p e c tra l S ig n a tu reV a r ia b i l i t y ." TRW IOC 4913 .7-71-193.
5 . E p p le r , W. G ., Helmke, C. A ., and Evans, R. H. "T able Look-UpApproach to P a t te rn R e c o g n itio n ." P ro c . Seventh I n t . Sym. on Remote Sensing o f th e Environm ent, 1971.
6. Remote M u lt is p e c tr a l Sensing in A g r ic u l tu re . Purdue U n iv e rs ityR esearch B u lle t in No. 844, 1968 and No. 873, 1970.
7. B auer, M. E . , Swain, P .H ., e t a l . "D e tec tio n of S outhern CornLeaf B lig h t by Remote Sensing T ech n iq u es ." P ro c . Seventh I n t .Sym. on Remote Sensing o f th e Environm ent, 1971.
8 . H o ffe r , R. M ., and G oodrich, F. E. " V a r ia tio n s in A utom aticC la s s i f i c a t io n over Extended Remote Sensing T est S i t e s . "P roc. Seventh I n t . Sym. on Remote Sensing of th e Environm ent, 1971.
9 . A nuta, P. E . , K r is to f , S. J . , e t a l . "C rop, S o il and G eo lo g ica lMapping from D ig it iz e d M u lt is p e c tr a l S a t e l l i t e P ho to g rap h y ." P roc. Seventh I n t . Sym. on Remote S ensing o f th e E nvironm ent, 1971.
10. S to n e r, E. R . , and H orvath , E. H. "The E f fe c t o f C u ltu ra l P ra c t ic e son M u ltis p e c tr a l Response from S u rface S o i l . " P roc . Seventh I n t . Sym. on Remote Sensing o f th e Environm ent, 1971.
11. Smedes, H. W., Lennerud, H. J . , e t a l . " D ig i ta l Computer Mappingby C lu s te r in g Techniques Using C olor F ilm as a T hree Band S e n so r." P roc. Seventh I n t . Sym. on Remote Sensing o f th e Env i r onment, 1971.
76
77
12. Smedes, H. W., S pencer, M. M ., and Thomson, F. J . "P re p ro cessin gof M u lt is p e c tr a l D ata and S im u la tion o f ERTS D ata Channels to Map Computer T e r ra in Maps o f a Y ellow stone N a tio n a l Park T est S i t e . " P ro c . Seventh I n t . Sym. on Remote Sensing o f th e Environm ent, 1971.
13. Bond, A. D, D asara th y , B. V ., and A tk inson , R. J . "F ea tu reS e le c tio n and Superv ised N on-Param etric C la s s i f i c a t io n A pplied to E arth R esources M u lt is p e c tr a l Scanner D a ta ." NASA C o n tra c to r R ep o rt, C on trac t NAS8-21805, 1971.
14. Wacker, A. C ., and Landgrebe, D. A. "B oundaries in M u lt is p e c tr a lImagery by C lu s te r in g ." IEEE Symposium on A daptive P ro c e sse s , 1970.
15. R oth, C. B . , and Baumgardner, M. F. " C o rre la t io n S tu d ie s w ithGround T ru th and M u lt is p e c tr a l D ata: E f fe c t o f S ize ofT ra in in g F ie ld ." P ro c . Seventh I n t . Sym. on Remote Sensing o f Environm ent, 1971.
16. B endat, J . S . , and P ie r s o l , A. G. Measurement and A n alysis o fRandom D a ta . New York: John W iley and Sons, I n c . , 1966.
17. Remote Sensing o f E a rth R esou rces, A L i te r a tu r e Survey w ith In d e x e s .NASA SP-7036, 1970.
18. Nagy, G ., S h e lto n , G ., and T o laba , J . "P ro ced u ra l Q uestions inS ig n a tu re A n a ly s is ." P roc . Seventh I n t . Sym. on Remote Sensing o f th e Environm ent, 1971.
19. Nagy, G ., and T o laba, J . "N onsupervised Crop C la s s i f ic a t io nthrough A irborne M u lt is p e c tr a l O b se rv a tio n s ." IBM J . Res.D ev., 1971.
20. A yres, F. M a tr ic e s . New York; Schaum P u b lish in g C o ., 1962.
21 K en d a ll, M. G ., and S tu a r t , A. The Advanced Theory o f S t a t i s t i c s ,Vol. 3. New York: H afner P u b lish in g C o ., 1966.
22. S ebestyen , G. S. D ecision-M aking P ro cesses in P a t te rn R e co g n itio n .New York; The M acm illan C o., 1962.
23. K eeping, E. S. In tro d u c t io n to S t a t i s t i c a l In fe re n c e . P r in c e to n ,New J e rs e y : D. Van N ostrand C o ., I n c . , 1962.
24. P h i l l i p s , M. R. " C o rre la t io n S ig n a tu re s o f Wet S o ils and Snows."IIT R esearch I n s t i t u t e F in a l Report J6243 -6 , NASA C on trac t NAS8-26797, 1972.
APPENDIX A
PROGRAM DESCRIPTION
The computer program s which u t i l i z e th e eq u a tio n s in th e t e x t a re
w r i t t e n in th e form of su b ro u tin e s and have been in c lu d ed as an in t e g r a l
p a r t o f a much la rg e r com puter program c a l le d an E a rth R esources
P ro c e sso r . This p ro c e sso r c o n ta in s s e v e ra l p re p ro c e s s in g and d a ta
d is p la y ro u tin e s in a d d i t io n to th e c l a s s i f i c a t i o n program s and i s
documented and flow c h a r te d in d e t a i l in th e f i n a l r e p o r t o f c o n tra c t
NAS8-26797 by IIT R esearch I n s t i t u t e , 10 West 35 th S t r e e t , C hicago,24
I l l i n o i s . Hence, on ly a b r i e f d e s c r ip t io n o f th e s e su b ro u tin e s w i l l
be g iv en . A sm all e x e c u tiv e program can be w r i t t e n f o r c o n t ro l l in g th e
sequence of c a l l in g th e se s u b ro u tin e s by fo llo w in g th e lo g ic flow
p re v io u s ly d e sc rib e d in F ig u re 2 and d isc u sse d in C hapter I I I o f th e
t e x t .
S u b ro u tin e BWNDR3
S u b ro u tin e BWNDR3 i s th e f i r s t s ta g e o f p ro c e s s in g o r th e
boundary program and re a d s th e raw d a ta ta p e as in p u t . This su b ro u tin e
c o n ta in s E quations (8) th ro u g n (16) in th e t e x t and th e lo g ic f o r u s in g
th e s e e q u a tio n s . The boundary program a lso c o n ta in s two s u b ro u tin e s
which w i l l be d is c u s se d . S u b ro u tin e GET6 i s used f o r g e t t in g th e d a ta
o f f d i g i t a l ta p e and p u t t in g i t in to th e com puter. The c o n te n t o f t h i s
78
79
su b ro u tin e has to be s p e c ia l iz e d to th e ty p e o f d i g i t a l ta p e form at
d e s ir e d . S u b ro u tin e JNTPB i s a j o i n t p r o b a b i l i ty d i s t r i b u t io n program ,
which w i l l be d isc u sse d n e x t .
S u b ro u tin e JNTPB
S ubrou tine JNTPB i s used f o r c a lc u la t in g th e j o i n t p r o b a b i l i ty
d i s t r i b u t io n o f s v e rsu s s in E quation (8) and th e d e c is io n r u le X y
as^ + bSy + c s^ s^ _< 1 , E quation (1 6 ). This program has a f ix e d s to ra g e
a l lo c a t io n , b u t th e shape of th e j o i n t d i s t r i b u t io n can be com plete ly
a r b i t r a r y because a se a rc h mode o f o p e ra tio n i s used r a th e r th an a ta b le
look-up p ro ced u re . This program w i l l a cc ep t d a ta o f any dynamic range
and o u tp u t a s c a t t e r d iagram bounded by th e minimum and maximum v a lu e s
o f th e d a ta . T his program c o n ta in s th re e su b ro u tin e s . S ub rou tine
DJCOBI i s an IBM l ib r a r y system su b ro u tin e fo r c a lc u la t in g th e e ig en
v a lu e s and e ig e n v e c to rs used in th e e l l i p s e e q u a tio n . S ub rou tine
LABELS i s used fo r la b e l in g th e axes o f th e s c a t t e r d iagram , w h ile
su b ro u tin e PLTBF6 i s s p e c ia l iz e d fo r use w ith th e S trom berg-C arlson 4020
p e r ip h e ra l equipment to o b ta in m icro film co p ies of th e boundary map.
S u b ro u tin e JNTPB a lso o u tp u ts th e boundary ta p e fo r u se in th e second
s ta g e o f p ro c e ss in g .
S u b ro u tin e CLASFY
S ubrou tine CLASFY c o n ta in s th e second, th i r d and fo u r th s ta g e s of
p ro c e ss in g v ia su b ro u tin e s TRUCK, SEQMRG, and CLASS, r e s p e c t iv e ly .
S u b ro u tin e CLASFY a ls o c o n tro ls th e number o f c l a s s i f i c a t i o n p asse s
d e s ire d and th e s iz e o f th e p x p c lu s t e r s e le c t io n a r ra y v ia s u b ro u tin e
TRUCK.
80
S u b ro u tin e TRUCK
The second s ta g e o f p ro cess in g i s su b ro u tin e TRUCK, which re a d s th e
boundary map ta p e as in p u t d a ta and lo c a te s th e homogeneous a re a s th a t
a re la rg e enough to c o n ta in a p x p a r r a y . T his su b ro u tin e a ls o
perform s th e s p a t i a l merging when two d i f f e r e n t c lu s te r s run to g e th e r .
The o u tp u t o f t h i s su b ro u tin e i s a boundary map ta p e c o n ta in in g th e
lo c a t io n o f th e i n i t i a l c l u s t e r s , which i s in p u t to th e th i r d s ta g e of
p ro c e s s in g . S u b rou tines LABELÀ and PLTBFA a re used fo r la b e lin g scan
and column numbers and o b ta in in g m ic ro film , r e s p e c t iv e ly , fo r th e v is u a l
d is p la y o f th e map o b ta in ed from su b ro u tin e TRUCK.
S ubrou tine SEQMRG
The th i r d s ta g e o f p ro cess in g i s su b ro u tin e SEQMRG and uses th e
boundary and c lu s te r lo c a tio n ta p e and th e raw d a ta ta p e as in p u t . The
boundary and c lu s t e r ta p s i s used to lo c a te and fe tc h raw d a ta belong ing
to each c l u s t e r . S t a t i s t i c s u t i l i z i n g E quations (17) through (30) a re
th en c a lc u la te d fo r each c lu s t e r and used fo r d ec id in g w hether to
s p e c t r a l ly merge c l u s t e r s . The c lu s t e r s a re read in s e q u e n t ia l ly , and
each new c lu s t e r has th e o p p o rtu n ity o f merging w ith any o r s e v e ra l of
th e p rev io u s c l u s t e r s . S u b rou tine SKRBIN i s an IBM system su b ro u tin e
and a llow s fo r sk ip p in g b in a ry re c o rd s on th e m agnetic ta p e . This
r o u t in e i s p r im a r ily used w ith th e c lu s t e r s e le c t io n s in c e th e c lu s te r s
may be lo c a te d anywhere on th e ta p e . S ub rou tine FETCOR i s used to f e tc h ,
c a lc u la te th e c e n tro id of each c lu s t e r and to c a lc u la te th e c ro ss channel
c o r r e la t io n s fo r each c l u s t e r . The means a re s u b tra c te d from th e
c o r r e la t io n s to form a co v arian ce m a tr ix in su b ro u tin e AMTRX, which
becomes an in p u t to th e e ig en v a lu e and e ig en v ec to r su b ro u tin e DJCOBI.
81
S ubrou tine ROTA i s a r o ta t io n m a trix c a lc u la t io n used to r o t a t e a
f e a tu r e v e c to r in to th e c o o rd in a te system o f a c l u s t e r . S ub rou tine
KCHECK i s used to check w hether th e c e n tro id s o f two c lu s te r s f a l l
w ith in each o th e r 's e l l ip s e s o r merge. I f two c lu s te r s w i l l merge,
th e s t a t i s t i c s of b o th c lu s t e r s a re combined and updated . The o u tp u t
o f SEQMRG i s a ta p e c o n ta in in g th e s t a t i s t i c s fo r th e f i n a l s e t of
c l a s s e s .
S ubrou tine FETCOR
In a d d itio n to fe tc h in g and c o r r e la t in g th e raw d a ta fo r each
c l u s t e r , su b ro u tin e FETCOR keeps t r a c k o f th e s t a r t i n g and sto p p in g
scan l in e s and columns o f th e c lu s te r s t h a t a re in th e com puter. This
in fo rm a tio n i s used w ith th e su b ro u tin e BSRECD, which i s an IBM system
l ib r a r y su b ro u tin e f o r back spacing re c o rd s . The u se o f t h i s su b ro u tin e
allow s f o r back spacing th e ta p e to f in d th e d a ta f o r th e n ex t c l u s t e r ,
r a th e r than rew inding th e e n t i r e ta p e and sea rch in g f o r th e n ex t
c l u s t e r 's d a ta .
S ub rou tine CLASS
The fo u r th s ta g e of p ro cess in g i s su b ro u tin e CLASS and u ses th e
ta p e c o n ta in in g th e s t a t i s t i c s fo r each c l a s s , th e boundary ta p e and
th e raw d a ta tape as in p u t . T his su b ro u tin e m ainly c o n ta in s E quation (31)
and th e p ro v is io n s f o r o u tp u t tin g th e c l a s s i f i c a t i o n map on s tan d a rd
computer p r in to u t o r m ic ro film . The c l a s s i f i c a t i o n map i s a lso ou tp u t
on tap e f o r use in su b ro u tin e CLASFY to o b ta in a d d i t io n a l c lu s te r s and
c l a s s i f i c a t i o n p a sse s .
APPENDIX B COMPUTER PROGRAM LISTINGS
SL'o ROU T T N f BV/NnR^r i j M F N S l O N X ( 1 2 » 2 5 6 ) » Y ( 1 ? » 2 5 6 ) » Mr H A N ( 1 2 ) »NN{ 2 5 6 ) » KS YM ( 4 9 ) , JSYM (
1 2 ^ 6 )n i ^^FNSI ON N W H I C H d ? )Na Mf L i S T / l N P U T 6 / N S r A N S > N 5 T A R T » N s P S » N C H » i ' J \ / A R » N S Y M , I S U M , N R T L G »
i M O D E f I T Y P F f M S F C » , N . 6 K I P , N B L K , I N C X » I N C Y , N S T X , N F T Y , N C R F N A M F L l S T / N C H ' J S F / N W M T r H F QU T V A L p Nc p ( N S r A N , N S r f t N S ) f Q U I V a L f Nt f ( N 5 T R T , N S T a RT) f Q U I V A L F N T F ( M r O L » N S P S )PQIJTVALFNCF ( NF HA N . N C H)I f A R n = 6 I P R I N T = 6 ï M T A P F = 1 0 Î 0 T A P F = 1 1R f a h C i r A R n , T N P l J T 6 )WRt T c ( t P R i N T » T N P U T 6 )R F A n ( i C A R n » N r H U S F )W R T T F ( l P R l N T , N r H U S F 1
1 F O R M A T ( I X , 7 1 4 )? f o r m a t ( I X , 12 11 )
rfao( rrARn,5 ) (.<syM( t ) , r = i , nsyM)6 F O R M A T ( 1 X , 6 0 A 1 )
MFLAG=0AV^=T5L!MA P O P = 0 , 0n x A V F = o , nD Y A V F z O . nD7 A V ' ^ = 0 , nN f a V=N!SCANI F ( N S K I P , F Q , 0) GO TO 9pn o 0 7 1 = 1 , N S K I PFALL S K R P I N ! T N T A P f , 1 , N OP )
0 7 C O N T I N U E OR C O N T I N UE
2 F O R MA T (1 HI )4 F0RMAT(5X,1I1II)
11 = 1K K = N 0 T R T - I
1 6 0 I F ( I I . f Q . N S F A N ) CO TO 510 1 1 = 1 1 + 1 NFLAC2=1 KK=KK+1! F ( I I . N F . 2 ) CO TO 9 0 0 0 0 1 7 0 J J = 1 , N C 0 Lc a l l g e t 6 ( X ( 1 , J J ) ,.n c o l , o , n c h a n , n s c a n o , i n t a p f , i e R R , n f l a g 2 , n s t R t ,
1 N p T L C , M O O F , N c R ' ^ , I T Y P F , M S F C )170 CONTINU"::9 0 0 C O M T I N U f
N F L A C 2 = 1no 0 0 0 J J = 1 , N C 0 Lc a l l G F T 6 ( Y ( 1 , J J ) , N r 0 L , 0 , N cH A N , N 5 C A N 0 , I i \ T A P r $ 1 F R R , N F L A C 2 , N S T R T ,
1 NPTLG,MOnF,NcRF,TTyPF,MSFC)'POO CON T I N UE
DO PRO J J = ? , N C O L
82
83
I J = J J - 1 X<i iM = 0 . 0 YC,I !M = 0 . 0 Z S U M c O . Ono 3 6 0 I C H A N = 1 , I S U M I r r H N = N W H I C H ( r C H A N )Xr , TFF = Y( T I CHN , J J )*-Y ( T ICHN , I J )Y n T F F = Y ( T I C H N , J J ) - X ( I I C H N , J J )XF!JM = XS!JM-} -Xni Fc: *xnTFF Y S U M = Y 5 U M + Y D T F F * Y n T F F ZSUM = Z 5 U . M + X n i F F * Y D T F F
3 6 0 r O N T T N U FX S U M = X S U M / A V Fy s u m = y s u m / a v e
Z S U M = Z S U M / A V F A P 0 P = A P 0 P + 1 . 0 a a = i . o / a p o pp p = 1 , 0 - A An X A V r = R q # n X AV'^ + A A^ YSUM OYAVF = R R * n Y A \ / F + A A^XSUM n Z A V R = P R * n Z A V F + A A * Z S U M XS U M ^ S Q R T ( X S U M )I F (XSUM , L T . F 3 . 4 ) GO TO 3 6 5
364 X.S'.IM = F 3 , 0 YFIJV! = F 3 , 0 GO TO 3 6 6
36 3 r O N T T N U FY S U M = S Q R T ( Y5UM)I F ( YSUY . L T . 3 3 . 4 ) GO TO 3 6 6 GO TO 3 6 4
3 6 6 C O N T I N U FCALL J N T P B ( YSUM, XSUM »Nf L AG »0 , 0 , K S Y M ( p ) , N P O P ,
? n X A V F , n Y A V F »P O Z A V F ,I J J , N S c a N , i I , N r O L » J S Y M , X , N 5 T R T » N N , i N r X )
n s c a n = n s a v
PRO C O N T I N U EDO 5 0 0 J J = 1 , N C 0 L DO 4 P 0 I C H A N = I » I S U M I i r H N = N W H T C H ( K H A N )X ( T I C H N , J J ) = Y ( I I C H M , J J )
4 0 0 C O N T I N U F 5 00 C O N T I N U E
GO TO 1 6 0 5 1 0 c o n t i n u e
NFLAG=1CALL J N T P B ( Y S U M , X S U M , N F L A G » 0 , 0 , K S Y M ( 3 ) , iM P 0 P ,
■?d x a v f , d y a v f ,P D 7 A V F ,1 J J , N S C A M , I I » N r O L » J S Y M , X , N 5 T R T » N N , l N c X )
REWI ND I O T A P R REWI ND I NTAP' ^
: CALL c l e a n
RETURN END
84S U P R O U T i N F L A B F L ^ , ( N S T A R T , N S T O P , r N c R F D T M F N S I O N I O U T ( 1 ? 0 )N n i F = ( N S T O P - N S T A R T + 1 ) / T N c R f T 1=0n o 1 r = N S T A R T » N S T O P , i N r R F IT = 11+1.I 0 U T ( T I ) = I / I 0 0 0
1 C O N T I N U FW R j T f ( 6 , 1 0 ) { r O U K T ) , 1 = 1 , N 0 T F )I 1 = 0DO ? I = N 5 T A R T » N S T 0 P , I N C R F IT=11+1I 0 U T ( T T ; = T / l O O - l / i n o o * i O
? C O N T I N U FWRt T f ( 6 , 1 0 ) ( T O U T ( I ) , I = 1 , N D I F )I 1 = 0DO B i = n s t a r t , n s t o p , i n c R f IT=IT+1T O l J T ( i n = I / l O - T / i n o * 1 0
? C O N T I N U FWRt T p ( 6 , 1 0 ) ( T O U T ( I ) , 1 = 1 , N D I F )I 1 = 0DO 4 I = N S T a R T , N S T O P , I N C R F I 1 = 1 T + 1l O U T d I ) = I - I / 1 0*1 0 I F ( l O U T ( I T ) , L F . 0 ) I 0 U T ( I I ) = 0
4 C O N T I N U FWR T T F ( 6 , 1 0 ) ( T0 U T ( I ) , 1 = 1 , N d I F )
10 f o r m a t ( 1 1 X , 1 ? 0 n )RFTURNF N n
85SUp RO U T t N f J N T P p ( n A T A H » n A T . â V » N F L A G » M î X » ' ' 1 r Y » A L P N n M , N P 0 P ,
?D X A V F * O Y A V P »P D Z A V F .T J J , N S C A N , l S r A N , N c O L , I S y M , N X , N 5 T R T » N N , l N C X Y )
OTMFNSr ON I . N r X Y d )DT^^PNSION NP{ >^A»F4) n y MF NSr ON D A T A ( 1 ? ) n T MF N S I O N T P I M ( ? 5 F )O l M F N S r O N I S Y M ( 1 ) , T O U l K 1 0 0 ) n i M F N S I O N N X ( 1 ) » N N ( 1 )DTMFNSr ON ALPNUM{ 1 ) , ALP h A ( T Z O ) , c O R n X ( 3 ) nOURLF P R E C I S I O N A ( ? . Z ) » F I G F M ( 2 » Z )I N T F G F R A L P N U M , A L P H A , PLANK DATA A S T R I K / 1 H * /DATA X M A R K / I H X /DATA R L A N K / 6 H /DATA N F L A G 4 / Q /
1 0 6 0 F 0 R M A T ( 4 8 X , ? 5 H D A T A SWI TCH HAS OCCURRED )1 0 6 1 F 0 R M A T ( 4 9 X , 3 0 H J 0 T N T PROr a R I L I T Y O I S T R I R U T I O N )1 0 6 ? F O R M A T d H l )1 0 6 3 f ORMa T ( 4 4 X , 1 1 h X - A X T S I S » T 6 » 6 X , l l H Y ' A X I S I S » 2 l 6 )1 0 6 6 f o r m a t ( 3 0 X » 6 H D X A V = ^ = » r l 5 , 7 » 6 H D Y A V F = , F l 5 , 7 , 6 H D Z A V P = » F l 5 , 7 )1 0 4 0 FORMAT! I H »67H MAXI MUM PROr a p I Î - T T Y Of f jNrOMMON a L I TY P X r F F D F n - r ONT
I I N U E F X r U T l O N , 2 1 6 )1 0 6 4 F O R M A T ! i x , 2 6 h SYMr OL N / S Y M r OL )1 0 6 5 f ORMa T ! 1 1 X , 1 2 1 ! 1 m * ) , / , 1 1 X , 1 h * , 5 5 X , 5 h P a RT , H , 4 H Of , 1 1 , 5 3 X , I H * , /
1 , T1X ,1?1 ! I H* ) )I F ! N F L A G 4 . G T , 0 ) GO TO 8 0 N F L G p =0
1 0 0 0 FORMAT ! I X , 4 7 A I )NFLGr ON I = ?I RW=1m r l g f n = o
I R T = l 1 n o 1 1=1 , 5 4 no 1 J = i , 5 4N P ! I , J ) =0
1 CON T I N UE r e w i n d I R TREWI ND IRW NFLAG4=1
8 0 c o n t i n u eI F I N F L A G . G T , 0 ) GO t o 13N G r D A T A V + l . 5NR = DATAH + T . 5I F ! NC . L T . 1 ) NC=1I F INR . L T . 1 ), NR = 1N P ! N R , N C ) = N P ! N R , N C ) + II = 5 4 * ! N C - 1 ) + N RI P I N ! J J ) = II F ! J J . L T . NCOL) GO TO 15 I P T M ! 1 ) = I R I N ! ? )WRt T p ! I R W ) ! I P T N ! I n , I 1 = 1 , N r O L )
15 CON T I N UE
8 6
R F T U R N I T C O N T I N U F I 7 C O N T I N U F
R F W I N D I R W I 0 P T = 1
I N = R IM = 7Rh O = 1 , 0 / ( 1 0 . 0 * * F >4 ( 1 , 1 ) = n X A V F
A ( ? , ? ) = n Y A V F A (1 » ? ) =nZAVF A ( ? » 1 ) = n Z A V FCALL n J r O R I ( A » T M , T N , I O P T , R h O , F R R » ' ^ I G F N )
C W R l T r ( 6 » l 0 6 7 ) A ( 1 ,1 ) » A ( 1 » 2 ) , I GFM ( 1 , 1 ) , F IGcN ( 1 , 7 )C WRt T f ( 6 » T C 6 7 ) a (2»1 ) » A ( 2 , 2 ) , f t f f N ( ? » 1 ) , F I G f N ( 2 , ? )
1 0 6 7 FORMAT ( l X » 2 > ^ l 5 , 7 , i n x » 2 F l 5 . 7 ) nXAVF=1. , n / A ( 1 »T ) n Y A V F = l , n / A ( 2 , 2 )A ( 1 , 1 ) = F T G P N ( 1 , l ) * n X A V F A ( 1 , 2 >=P^TGFN( 2 , l ) * n X A V F A ( 7 , 1 ) = F i G c N ( 1 , 7 ) * n Y A V F
A ( 7 , 7 ) = r i G F N ( 2 , 2 ) * n Y A V FnXAVF = FTr,FN (1 »1 ) * A ( V 1 ) -i-FTG<^N(1 »2 ) * A ( 2 , 1 )OY A VF = F I GFN ( ? ♦ I ) * A ( 1 .. 7 ) +e IGFM ( 2 » 2 ) A ( 2 , 2 )nZAVF = F I GFN ( 1 »1 ) * A ( 1 » 2 ) + F I G F N ( l » 2 ) * A ( 2 , 2 ) + F i G = ' N ( 2 , l y * A ( l » l )
1 + F T G F N ( 2 » 2 ) * A ( ? , 1 )W R t T f ( 6 , 1 0 6 6 i n X A V F , 0 Y A V F » n Z A V F 1=0n o i o n N c = i , 6 4DO 1 TO NR = I , 6 4 Î = 1 + 1I F ( N P ( N R , N r ) , F 0 . 0 ) GO TO I TO XXX=MR* NRy y y = n c * n c
Z Z Z = N R * . N C
G U M = n X A V F * X X X + n Y A V F * Y Y Y 1 + D 7 A V F * Z Z Z
I F ( S U M , G F . 1 . 0 ) G 0 t o 1 16 N X ( I 1=0 G O T O 1 6 0
1 1 6 N X ( I 1 = - l1 6 0 C O N T I N U F
WRiTF ( 6 , 1 0 6 ? 1 WRTTF ( 6 , 1 0 6 1 )W R l T p { 6 , l 066 1 n X A V F , D Y A V F , n Z A V F W R I T F ( 6 , 1 0 6 4 )
C CALCi i LATF TAPLFm a x k n t = o
DO 2 2 N C = 1 , 6 T DO 22 N R = 1 , 6 TI F ( M P ( N R , N C ) . G T . MAX<NT) M A X K N T = N P ( N R , N C )
22 C O N T I N U FI F ( MaXKNT . L T . 4 6 ) ,YaXKNT = 46 , N F A C T = M A X K N T / 4 6
X X X = F L O a T ( M A X K N T ) / 4 A . 0
87
NFAC=0I F ( NF ACr . L T . 1) MFACT=1 W R T T F ( 6 * 1 0 5 0 ) P L a N < , N F A C NFAC=NFAr +NFACT00 1 = 1 , 4 6W R T T r ( 6 , l 0 5 0 ) ALPNI IM ( T ) »NFAC
1 0 5 0 f o r m a t ( 5 X , A 6 , 6 X , I 6 )N F A r = N F A r + N F A r i
99 CONTINUFWR T T r ( 6 , 1 O A ? )
: P R I NT D I S T R I R U T I O M ON PAGFr O R D X { 1 ) = 0 , 0 r O R O X ( 7 ) = r O R O X ( l ) + 6 0 . 0 r O R o x ( 5 ) = r O R o x { 1 ) + 1 1 0 , 0
1 0 9 1 f o r m a t ( 1 h i )
n o I F Mn = 1 , 5 4M r = 5 5 - i F N nn o 6 6 1 = 1 , 5 4 A L P H A ( I ) = R L A N K
6 6 C O N T I N U FI F ( NF L G . F Q , 1 ) GO TO 6 0 DO 65 1 = 1 , 5 4
T r t N { I ) = n 6 5 C O N T I N U F69 COMTINUF
n o 64 N R = 1 , 5 4XX = F L 0 A T ( N P ( N R , N C ) )I F (NFLG . F Q . 1 ) GO TO 911 P I N ( N R ) = N P ( N R , N C )
91 CONTINUFI C A R = X X + ( 1 . 0 0 1 - 1 . n / X X X )I F ( I CAR . G T , 46 ) TCAR=46 A L P H A ( N R ) =AL PNUW( I C A R )
64 COMTINUF CORDY=FLOAT(NC)YMARG=XMARKI F (NC . N F . 5 4 - I F N n / l 0 * 1 0 ) YMa R G = A S T R i K . W R l T F ( 6 , l 0 0 8 ) r O R O Y , Y M A R G , ( A L P H A ( I ) , I = 1 , 5 4 )
10 08 f ORMa T ( 1 X , F 8 . 1 , 2 X , A 1 , l ? O A l )65 C O N T I N U F
W R l T F ( 6 , 1 O l 0 )W R t T f ( 6 , l O l l ) r 0 R 0 X ( 1 ) , r O R n X ( 2 ) , c O R n X ( 3 )
1011 f o r m a t ( 6 X , F 1 0 . 4 , 5 0 X , F 1 0 . 4 , 4 0 X , F 1 0 . 4 )NFLG=1V'RI TF ( 6 , 1 06 2 )N5l , iR=lLK'FR=iLOW=NSTRT
70 5 CONTINUFNh I = L 0 W + 1 2 0 - 1N I J P P F R = L W F R + 1 2 0 - 1I F (NUPPFR . G T . NCOL) NUPPFR=NCOLW R I T F ( 6 , 1 0 6 2 )CALL L A P F L 6 ( L O W , N h I ,1 ) no 191 1 1 = N l , N S r A N
8 8
R F A D ( I R W ) ( T R î N( J J ) « J J ^ l » NC0 I . )DO 1R5 J J = 1 » N C 0 L r r H F C K = I P I N ( J J )J C H E C K = N X ( I C H F C K )TF ( J C H F C K . N F . 0 ) GO TO 1 1 7 I S Y M ( J J ) = A L P N U M ( N S U R - 1 )N N ( J J ) = 0 GO TO 1 RR
11 7 I S Y M ( J J ) = A L P N U M ( N S I J R )N N ( J J ) = —1
1 RR C O N T I N U FI F ( NF L GF N . N F . 0 ) GO TO 1R6 W R I T F ( I R T ) ( N N ( J J ) , J J = i , N C O L )c a l l P L T p F 6 ( l S Y M , N r O L , N R L K , T N c X Y ( l ) » l N r X Y ( ? ) » l N r X Y ( R ) ,
1 i N r X Y ( A ) »NCR'=')I R A C O N T I N U F
WRt T c { 6 > 1 Ü R 6 ) 11 » ( T S Y M ( J J ) ♦ J J = LWPR»N U P P F R )1 0 3 6 FORMa T ( 5 X » T 6 , 1 2 0 a 1 ) l ORR F 0 RMa T ( 1 X » I 6 )1 3 1 C O N T I N U F
NFLGFN=1r e w i n d IRWLWFR=NUPPFR+1L 0 W = N H I + 1I F ( NUPPFR . L T . NCOL) GO TO TOR
9 9 5 CON T I N UEl O l 0 format ( 1 1 X, 1 2 ( 1 O H X *********))
NF LGF Nr ORFTURNEND
CM
X H- m I/;
_I > - yj
(\l O'_ 1 X - I.
<-i z
CM •> >-H Z » <CO X
O U) CK Z
• " <t.
— cCM cn
_J OL
o ^I — 1 C O
t - z_j •>«' u.
O' q; H- VJ_J z*—I <1
Ol00CO CO <- Q. '— CO < Zs: *C '' « -O ' CO <t
* - < :CM X «-< Q. - _l
CO «■a- »>- QZ CM
<l '—Itr «- X X X X
I CMCC œ <t <c _j _J
CO<_JuÜJ
XXX
X » f - X Cl «—X o •>f— I— li.; • CO O
Z O t- — X
- c_Z IL < r C O XX V «'z uI— •'CL CO CO X Z I-<t #—u C •>CO u
z * z c•I CO •' O X CO CO X X <1. CL -CO Q. CO cr Z Z Z _I •> X X X X CO < a U UJ X z Z CO 3 « «-I cO CL Q.•> < z oX CL — X U X X CO Z X X z »-i CO CO •>
IL-orKJz•' X _/ <1- XI— CO ZViLCOIDCLX
00
3 Z ZOOO •'QZCDQ I _J CCû Z Z Z c o < r _ i « - i i ü i L < c c 5 : Z ' - t x x x : z 5 : x 3 0 0 x c o i r . c o < i < i c o CO CC^_IZZZZZZ
cXCL_J<r
X — —• <C —' X CO <r X X Ll X 3 ^
CO 3 CL vO •> CO CL z oX < z •- c
X Cl X » I— I
X vO •*•— IP, If'. --- LO
X C O X c X C <t »— <l CO IL IL QZ Lc Z OZ QZ 2: ÛZ (M
ICO+ XX z c/ ; CO < 3
X 3I— C _ '
— zX IIc XOZou.vC'co
<uCOzIICOz < ! c_COz
uzII3c_
Z CO —' *-H CO
•> <X CLz zCO 3 CO O »C MZ «-I
Ol •'Z X •>•V COX 3 XCO 3 Z3 3 33 Z O r-l3 — X +Z «-XX — CD Z Z X QZ CO 3 33 5: CCI O O3 O < X X 3QZ ID 3 II II 3X CO 3 X 3 Z ZCO 3 — OZ3 3 3 3 X X 3J 3 •- Z X O O <I < < 3 Z O U Z
' 0 3 '3 3 Z«— 3 QZID
90SU o.ROUT î Np T R U r K { N r r N T » N P A S S )D I M E N S I O N N N A O r f 1 2 , 2 5 6 ) , M T A P ( 1 1 ) , I P R T ( 2 5 6 ) , I P L O T ( 2 5 6 )D I M E N S I O N N T P L ( 4 0 0 )rOMMON / L A P 1 / X o a R ( 4 P * 1 2 ) »S TT-Ma ( 43 » I 2 ) , RÜT( 4 3 » 12, » 12 ) rOMMON / L A 0 2 / X ( 1 2 ) , N S Y M ( 4 9 ) , N S P S , N S r ANS , N f H a N , l't 9 , L T I D , LT 11 , L t 12 ,
1 L T 1 3 , L T 1 , I X X X , T Y Y Y , i N S T A R T . N S T O P ,I N n J L G . M O D F » U Y P F , M S ^ C » 14 , N c R E »I N S K I P , l N r X , l N c Y , N S r X » N S T Y
N F L G X X= 0 N F L A G X = 0 REWI ND L T l l R p y i N D L I T N F L A G i =0 M EI N=0I X T Y = I X X X * I Y Y Y DO 10 1 = 1 , l Y Y Y MTAP f I ) = I
10 C O N T I N U EDO 50 1 = 1 , 4 0 0 NTRL( I ) =I
50 C O N T I N U FPO 11 1 = 1 , l Y Y YR F & D ( L T l l ) ( MN a c C ( t , J J ) » J J = 1 » N S P S ) m E T N = M F I M + 1
11 C O N T I N U ENl jP = N S P S - I X X X + 1n c n t = n c c m t + iNFLAG=0
?0 0 CONTINUFT T t = M T A P ( 1 )DO 1 1 0 J J = 1 , N S P SI F ( J J . G T . NUP) r o TO 10?I J = J JJ I = J J + I X X X - 1 N7FR0=n I K N T = n I FI !Mr?0 J l J r M T A P ( 1 )MTFMP= NCCNT+1 DO 1 Ol T = U , J I DO 1 0 0 J I J = 1 , I Y Y Y I I J = M T A R ( J I J )I F ( N N A C C d l J , ! ) . L E . MCCNT . A N D . NNACC( 11 J , I ) . N E . 0 ) GO TO 1^ 2 TF ( N N A F r ( T i J , n ) 1 0 2 , 1 0 7 , 1 0 6
1 0 6 I F ( N N A C C ( I I J , n . r - T . NT^^MP) NT'^MP = NNArC ( I I J , I )GO TO 1 0 0
1 0 7 n z f r o = m z e r o + i
1 0 0 C O N T I N UE1 0 1 c o n t i n u e
I F ( NZERO . N F . I X T Y ) GO TO 1 0 5 DO 1 03. 1 = 1 J , J I DO 1 0 4 J I J = 1 , I Y Y Y NNACF( J U * î ) = N r N T
1 0 4 CONTINUF
91
1 0 ? r O N T l N U PN r N T = N C N T + li r ( N r N T , G T , 4 OO) GO TO Q9Q GO TO 11 0
i n ' ; CONTI NUEDO 10? ! = I J , J I n o 10? J T j = l , l Y Y YI F ( N N A C C ( J I J » n . F O . 0 ) N N A C C C J I J » I ) = N T f m P
10? CONTI NUE GO TO n o
10? CONT I NUE n o CON T I N UE
no 111 J J = 1 , M S P 5n ( J J , f Q , NSPS ) r O TO 111I F ( N N A C C n I F ( M N A C C d I F ( N N A C C ( I I F ( N N A C C I I I F ( M N A C C d i J ^ N N A C C ( I I J I = N N a C C ( I I
I > J J ) . L E . ■ NCCNT ) GO TO H I I » J J + n . L F , NCCNT) GO TO 1 11 T , J J ) . L F . 0 ) GO TO 1.1 1 I »JJ + 1 ) . L F . 0) GO TO i n I » J J ) . F Q . N N A C C ( 1 1 1 » J J + 1 ) ) GO TO 1 1 1 » J J )» J J +1 )
I F ( JT . r n . 4 0 0 . O R . I J . G T . 4 0 0 ) r-0 TO 111 I F ( N T A L f J l ) . G T . N T F L ( T J ) ) 0 0 TO 1?? N T n L ( î J ) = N T n L ( J î )GO TO 111
1?F CONTI NUFN T 9 L ( J I ) = N T r L d j )
111 CONT I NUE 100-7 f o r m a t ( 1 X , I G )
V ' R t T f ( L T i ) ( N N A C r ( n i » J J ) , J J = 1 »N.SPS)1 F (VF I N . G F , NSfam. F) r,0 TO 0 9 9 lYT =iVTAq ( 1 )R c A D l L T l l ) ( N N A C C ( T Y I , J J ) »J J = 1 » N 5 P 5 )v f t N = m f I N + 1
N T F M P r M T A B ( 1 )I Y Y = I Y Y Y - 1 no 1 ? 1 1 = 1 , l Y Y Mt.aB ( I ) =MT Aq ( T + 1 )
m C ON T I N UFV T A F ( I Y Y Y ) c N T ^ v p GO TO ? 0 0
9 9 0 CONTI NUEno 1 ?? 1 = 2 » I Y Y YI I i =NTAB ( I )n o 1 1 ? J J = 1 , NSPFIF ( J J . r Q , NSPS ) r o TO 1 1 ?I F (MM ACC ( I I F ( M N A C C d I F (NNACC ( I
T » J J ) . L F . N r C MT ) GO TO 11?I , J J + 1 ) . L F , N C C N T ) GO TO 11?I »J J ) . I F . 0 ) GO TO 11 ?I , J J + 1 ) . L E . 0 ) GO TO 1 1.2 I , J J ) . F Q . N N A C C ( I I I » J J + 1 ) ) GO TO 1 1 2 » J J ), J J + 1 )
I F ( J I . F T . 4 0 0 . O R , I J . G T . 4 0 0 ) FQ TO 1 1 2 IF ( N T q L ( J I ) .FT. N T % L ( I J ) ) GO TO 1 2 6
I F ( N N A C C ( I I F ( M N A C C d I J = NNACC( I I J I = N N A C C ( I I
92iMTnL( î J ) = N T r L ( JT )GO T O . 11?
1 ?6 CONT I NUEN T B L C J I ) = N T B L ( T J )
1 1 ? CON T I N UEW R i T F ( L T i ) ( N N a c c ( I T I » J J ) »JJ = 1 »NSPS)
1?? c o n t i n u eFNn F I L F L T 1 RFWI ND L T l REWi Nn L T l l R F V I N O L T I ?W R l T r ( 6 , l 0 0 7 ) ( N T o L ( I ) , 1 = 1 , 4 0 0 ) no 1 1 1 1 = 1 , 4 0 0IF ( N T R L ( I ) . F Q . I ) no TO 11?J I = ! + 1I -^ ( N T P L ( J I ) . N E . I ) r o TO 1 1 4 N T R L ( J I ) = N T R L ( I )
1 1 4 CON T I N UE 11 ? CON T I N UE
11 = 1MTEMP = I !no 1 1 6 I = ? , 4 0 0I F ( N T r L ( I ) - N T d L ( T - 1 ) ) 1 1 7 , 1 I E , 1 19
1 1 9 I F ( M T R L ( T ) . N F . I ) GO TO 1 1 7N T R L ( I - l ) = n t e m p I 1 = 1 I + i N T F M P = I I GO TO 1 1 6
1 1 q NTRL ( I - l ) =NTF;yp GO TO 1 1 6
1 1 7 N = N T f L ( I )N T o L ( I - l ) =NTFMP M T F M P = N T P L { N )
1 1 6 c o n t i n u e
N T R L ( 4 0 0 ) = NTFMPW R I T f ( 6 , 1 0 0 7 ) ( N T r L ( I ) , 1 = 1 , 4 0 0 )L ''I F R = 1 LOV' = N S T A R T
7 0 F FONT I NUEN!.iP P f R=LWf R + i ? 0 - i Nh t = L O w + i ? 0 - iI E ( NUPPFR . G T . N5PS ) NUPPFR=NSPSl n i E = N U P P F R - L W F R + iW R I T E ( 6 , 1 3 3 5 )
1 0 0 5 F O R MA T (1 H I )CALL L A R F L A ( L O W , N h I , 1 )no 7 1 0 1 1 = 1 , N SC A N 6Rf a n ( L T l ) ( N N A F G ( 1 , J J ) , J J = 1 , N S P S )no 1 1 5 J J = 1 , N S P SI R = N N A C C ( 1 » J J )I F ( I R .LF. 0 ) GO TO 115 N N A C C ( 1 »J J ) = N T R L ( I R )
1 1 5 C O N T I N U FI F ( NELGXX . G T . 0 ) GO TO 1 ?7 WRt T f ( L T l ? ) (NNACC ( 1 , J J ) , J J = l ,N.SP.5)
93
1 P 7 rOMTI . MUF J I = 0DO 7 1 1 J J = L WHR » N UP P F R JT = J I + 1M = NiMACC ( 1 » J J ) - ( i MNAr r ( i , J J ) - i ) / 4 K * 4 % + ? J P R T ( J J ) = : N S Y M ( M )I P L O T ( J ! ) = N S Y M ( N )
711 r OMT T NUPW R t T f ( 6 » 1 0G3 ) T I ♦ ( t P R K J J ) , J J = LWFR »NI JPPfR )CALL P L I R F A ( I P L O T , I D I F » N r L K , T N C X » I N c Y , M S T X , N S T Y ,
1 N C R F » N F L A G X , N F L A G 1 )1 0 0 3 F O R M A T ( 4 X , 1 6 , 1 H * , 1 ? 0 A 1 )7 1 0 C O N T I N U F
RF' - ' IND L T l NPLAC-X = C Np LGXX=1 N P L A G 1 = 0l w f r = m u p p f r + iL 0 W = N H I + 1I F ( NUP PF R . L T . NSPS ) GO TO 7 0 5
5 7 0 C O N T I N U Fn c c n t = n c n t - iFNn F I L P L T l ?Rp WI ND L T l ?REWI ND L T l I X X X = I X X X - 4 I Y Y Y = I Y Y Y - 4 L T l 1 = 1 3r f t u r n
^ND
94SUr ROü T i N t S F O M R n ( N r L U S T , K O U N T , r N î T C L )rOMMON / L û r 1 / X o 4 R ( 4 3 » 1 2 ) » S I F M A ( 4 3 , 1 2 ) , R 0 T ( 4 3 , 1 2 , 1 2 )rOMMON / L A R 2 / X ( 1 2 ) , a L P h A ' 4 9 ) , N S P S »N SC A NS, Nc H A N , L T 9 , L T l 0 , L T 11 »L T 12 »
I L T 1 3 , L T 1 , I X X X , I Y Y Y ,1 N S T A R T , N S T 0 P ,1 N r T L G » M 0 d F » I T Y P r »MSf C » I 4 , N c RE»I N S K I P , I N C X » I N C Y » N S T X » N S T Y
nOURLF P R F C I S I O N A ( 1 2 » 1 2 ) » F î R F N ( 1 2 » 1 2 )OTMFNSTON M F R n r f Z n n ) , M P 0 P ( 2 0 0 ) » N r X F r ( 2 0 ) » C ( 4 3 » 7 8 ) » F ( 1 2 * 1 2 ) n i M F M S i O N C 0 V ( ? 4 )F O ' J î V â L F N r F ( r O M ( 1 ) , N S P S )
1 0 0 0 r 0 R V a T ( 1 X , i 6 » 1 2 F 1 0 ^ t )1 0 0 1 f o r m a t ( 1 X , 4 h XRAR )1 0 0 2 f o r m a t ( I X » 1 6 H D Î 0 NOT r ONVFRO )1 0 0 3 f o r m a t ( 1 X »7Hr ( "L l JST= , J6 » 1 4MMFRr,c ( 7 r L ! 1ST J = , 7 6 )1 0 0 4 FORMAT ( 1 X , 5 h RmO= , 1 5 . 7 , 5 hi ^RR= , f 1 5 , 7 )1 0 0 3 FORMAT ( l X , T ? c i n , A ,1 0 0 6 F O R MA T ( I X , 1 2 T S )1 0 0 7 FORMAT ( 1 X , 23HVFROT A'O W I L L TA<F PLACE )TGÜB F O R MA T (1 H )1 0 0 9 f o r m a t ( 1 3 H r o v e Ma t r i x )1 0 1 0 f o r m a t ( 1 2 H NORM r i c R N )1 0 1 1 f o r m a t ( i r h p . A . r o v . M a t r i x )1 0 1 2 f O R M a T ( 1 h , 6 haSUM= , r i 5 . 7 , 7 H r L U S T r p , 7 4 )1 0 1 3 f o r m a t ( 1 X , 2 8 M X n A R (7 , J ) , J=1 , 1 2 ) , T = 1»KOUNT )1 0 1 4 FORMAT ( 1X , 2 9mS T6M, a ( 7 , J ) , J = 1 , 1 2 ) , T = 1 , K 0 U N T )1 0 1 5 FORMAT ( 1 X , 5 5 h ROT ( I , î CM AN , J C m a N ) , JCH AN = 1 , 1 2 ) » I CM AN = 1 , 1 2 ) , I = 1 , KOI 'NT
1 ) )
1 0 1 6 f o r m a t ( I X , 1 6 , ( 1 2 ^ 1 0 . 3 ) )N F LG = 0r Z F C H = F L O A T ( N om A N ) - 2 . 0 R F U I MO L T I O R F ^ I N O L T 1 9 Rm O = i , 0 / ( 1 0 . 0 * * 3 )] F ( M S K I P » F O . 0 ) r-0 TO 60 0 7 1 = 1 , N S K J PCALL S < R f T N ( L T i O , 1 , N O P )
7 C O N T I N U F6 C O N T I N U F
0 0 3 I C L U S T = 1 , N C L I J f t v,crRr,r( i c L U S T ) = i r L U S T
3 CONTI NU' ^1 ^ ^ N r H A N I N = I M I 0 P T = 10 0 10 I C L U S T = I N I T C L , N C L U S T I F ( N f L O , C T . 0 ) GO TO 11 I F (KOUNT . C F . 4 3 ) GO TO nk o m n t = k o i .i n t + iI FLAC- =K0UMT ■CALL F F T C O R ( T F L A G , C , MROP, Nf l G , I N î TCL ' )WR I T f ( 6 , 1 0 0 1 )W R i T f ( 6 , 1 ü ü O ) I FLAC- , ( X7AR( 7 f l a g , ! ) , 1 = 1 , 1 2 )Ml =1 MJ = 1?
95VK = 1 ? n o 500W R T T F ( 6 , l 0 0 0 ) TFLAO» ( r ( I F L A r , , M R ) , MR= Mt , M J )
5 0 0 C O N T I N U FCALL AMTRX ( I F L A G * X R A R , C » A , N C H A N ) w R t T P ( 6 » 1 0 0 8 )V R T T p ( 6 » i O O o )WRt T p ( 6 » 1 0 0 5 ) ( { A(MT » M J ) » M J = 1 » 1 2 ) »MI = 1 , 1 2 )CALL n J C O R I ( A , I M , T N , l O P T , R u O , F R R , r i G F N ) WRt T f ( 6 » 1 . 0 0 4 ) Rh O » f RRW R T l F ( 6 » l t - 0 5 ) ( ( a ( M T , M J ) »MJ = 1 » 1 2 ) , ^ 1 = 1 , 1 2 ) H R I T F ( 6 , I 0 0 8 )W R T T r ( 6 , l 0 0 5 ) ( ( F T F f N ( v T , M J ) , MJ = 1 , 1 . 2 ) , M l = l , 1 2 ) I F ( cRR . F Q . 0 . 0 ) CO TO 15 M r R c r ( t c L U S T ) = 0k o i j n t = k o u n t - i v R t T F ( 6 , 1 0 0 ? )CO TO 10
15 C O N T I N U FCALL ROTA ( I FL AG , RO T , F I CRN , MCH AN , A , S I CiV A )Mf r g f ( I C L U S T ) =KOl )NTyRT Tc ( 6 ,T 0 0 ) TCLUFT , M r R c c ( | r L U . 5 T )MPOP ( < OUNT ) =v i POP( I C L U S T )I F ( KOUNT , F 0 . 1 ) CO TO 10M C L U S T = K 0 U N T - 1no 2 0 I CHF CK = 1 , 2 0N F X f c ( I C H C T K ) = 0
2 0 C O N T I N U E MCHFCK=1n o 25 J C L U S T =:1 ,NCL! 1STTf ( V c r g p ( j c l u S T ) . L T . M C H f ^ C K l c O TO 25’'■Vm f c K = MCHFCK + iTc ( V F R G c-( J F L U S T ) . r Q . KOUNT) GO TO 2 6 J ^ L AG = N f RG=’ ( JCLUST ) n o 80 ICHAN = 1 ,NCHANX ( T C H A N ) = X R A R ( J F L A C , I c h a n ) - X 8 A R ( K O U N T , I CHAN)
-70 C O N T I N UETr LAG=KOUNTc a l l K C H F C K ( I F L A C , R 0 T , X , S I C M A , A S U M , M C H A N )'■'R T TF ( 5 , 1 OOr )WR T T< ( 6 , 1 01 2 ) a S U M , J F L A CI F ( A S J V . G T . c Z f c h ) CO TO 2 5I F L A C = J F L A GCALL K C H ^ c K l I F L A G , R O T , X , S I GMA , ASUM, NCHAN)HR I T F ( 6 , 1 0 0 8 )H R l T F ( 6 ,1 01.7 ) A S U M , J F L A G TC (ASUM . C T . C Z ^ C H ) CO TO 25 N E X F c ( 1 ) = N F X r C ( 1 ) +1 N. f i i p = NFXFC ( 1 ) + 1
N f x f c ( N S U R ) = J F L A G 2 5 C O N T I N U F2 6 I F ( N r X F Ç ( i ) . F Q . 0 ) GO TO 10
no 501 KK=l , N5UR
96W R t T p ( 6 >1 0 0 6 ) K K , N f x F C ( K K )
501 CONTI NUEM S U P = N F X F C ( 1 )+1 TO T A L = MP O P ( KOUNT)OO 31 I R U N = 2 » M S U R N S U P = N F X F C ( TRUN)SUM=v!POP(NSUB)T 0 T A L = T 0 T A L + S U M
31 C O N T I N UF INl ' MsOH F M - V P O P ( K O U M T ) no '3 3 I c h AN = 1. »NCMANX ( I C H A N ) = X R A R ( K O U N T , I C H A N ) * O P N / T O T A L no 4 0 J CH A N = I C H A N , N C H A N I N U M r l N t j y + ln { T t h a n , J C H A N ) = C ( KOUNT, I N U M ) * 0 F N / T O T A L
40 CONTI NUE 33 CONTI NUE
no 4= I RUN=?, M. SUR N S U R = N F X F C ( T R U N )I NUM= 0n P N r W P O P ( N S U P ) no 50 I C H A N = 1 , N C H A NX ( TCHAN) =X { I C H A . N ) + X ' ^ A R ( N S U n , T C H A N ) * n r M / T O T A Lno 33 J C H A N = i r u A N , N r H A NI NUy= l N i . J M+ lP f I C H A N , J C H A N ) = R ( I C " A N , J C H A N ) + C ( N S U B , I N U V ) * n F N / T O T A L
5 5 C O N T I N UF 50 CONT I NUE 45 CONTI NUE
no 6 0 I CHAN = 1 , NCHAN no 65 JCHAN = ICHAN ,NOHAMA ( ! C H A N , J C H A N ) = R ( i r H A N , J C H A N ) - X ( T C H A N ) * X ( J C H A N )A ( JCHAN , TCHAN ) = A ( T ri - i / \N, JCHAN )
65 CON T I N UF 60 CONTI NUE
W R T T F ( 6 , l 0 0 q )W R l T F ( 6 , l 0 0 5 | ( ( A ( W T , M J ) , M J = ! , 1 ? ) , H l = l , l ? ;CALL n J C C P I ( A , l M , l M , l O P T , R H O , E R R , n i G F N )W R I T E ( 6 , 1 0 0 4 ) R H O , c p RWR T T f ( 6 , 1 0 0 3 ) ( ( A ( M T , y j ) , MJ= 1 ,1. 2 ) » y I = 1 ,1- 2 )H R I T F ( 6 , 1 O O B )WRTTF ( 6 , 1 0 0 5 ) ( ( t ^ i r r N ( Mi , M J 1 , MJ = 1 , 1 2 ) , M I = 1 , 1 2 )I E ( cRR . N F . 0 , 0 ) r-O TO 10 W R I T E ( 6 , 1 0 0 7 )I E L A G = N f X F C ( 2 )M P O P ( I E L A G ) = T O T A LI NUMr Ono 70 l C H A N = i , N C H A NX R A R ( T ELAG, ICHAN ) = X ( i r u A N )nn 75 JCHAA'= I F maai ,MFHAMI N U M= I N U M + 1C( I E L A G , I N U M ) = P ( I C H A N , J C H A N )
7 5 CONTI NUE 70 CONTI NUE
97C A L L R O T A ( I F L A G » R O T » !^T G E N , N f H AN » A » S I G M A )D O R O j c l u s t = i , n c l u ? t
D O R F I R U N = ? , M 5 U R N S U R = N R X F C ( I R U N )I F ( M F R G F ( J C L U S T ) . N F . N S U R ) GO T O 8 5 M F R G F ( J C L U S T ) = I F L A G
8 5 C O N T I N U E 8 0 C O N T I N U E
m e r g e ( I C L U S T ) = T f l a g I F ( N F X F C ( 1 ) . F Q . T ) G 0 T O 9 4 I S W = 0 J C H F C K = ID O 9 0 J C L U S T = 1 , N C L U 5 T I O U M s M E R G F ( J C L U S T )
9 1 I F ( M f R G E ( J C L U S T ) . L T . J C H E C K ) C O T O 9 0 I F ( M f R G F ( J C L U S T ) . r - T . J r H F C K ) c O T O 9 2 T F ( I S W . f Q . T ) G 0 t o n ?J r M F r K = J r H F C K + T T F ( J C H F C K . F 0 . K 0 U N T ) ^ 0 TO 9 4G O T O 9 0
9 2 M F R G ^ I J C L U S T ) = M F R G f ( J c L U S T ) - ]I S W =1G O T O 9 1
9 3 I F ( J C H F C K . G T . K O U N T ) G O T C 9 4 I c w = nI N ! i M = 0
M P O P ( J C H F C K ) = M P O P ( T D U ^ n n o 9 9 T r H A N = l » N C H A NX B A R ( J C H E C K » I CHAN) = X B A R ( I D U M » I C H A N )S I G M A ( J C H E C K , I C H A N ) = S I G M A ( I D U M , I C H A N )
D O 1 0 0 J C H A N = I C H A N , M C H A Ni n i j h = i n u m + i
r ( J c h f c K » i N t j M ) = r ( t o u M , T NUM )
R O T ( J C H E C K , I C H A N , J C H A N ) = R O T ( I D U M , I C H A N , J C H A N )R O T ( J C H E C K , J C H A N , I C H A N ) = R O T ( I D U '.S J C H A N > I C H AM )
1 0 0 C O N T I N U E 9 5 C O N T I N U F
D O 9 6 L C L U S T = 1 , N C L U S TI F ( M F R G F ( L C L U S T ) . N f . i n U M ) G O T O 9 6
m e r g e ( L C L U S T ) = J C H E C K
Of , c o n t i n u e
J r H E C K = J C H ' ^ C K + 1
9 0 C O N T I N U E
9 4 K 0 U N T = K 0 U N T - N F X F C ( 1 )1 0 C O N T I N U E n C O N T I N U E
W R I T f ( L T 9 ) ( c 0 M ( T ) , 1 = 1 , ? 4 )W R t T f ( L T 9 ) ( { X d a R ( I , J ) , 1 = 1 , K O U N T ) , J = 1 , 1 2 )W R t T f ( L T o ) ( ( S t g M a ( T , J ) , 1 = 1 , K O U N T ) , J = 1 , 1 7 )W R l T r ( L T 9 ) ( ( ( R O T ( T , l C H A N , J f h a N ) , I = 1 , KOU N T ) , TCM A N= 1 , Nc h A N ) ,
1 JCHAN = 1 , NCHAN)W R l T c ( 6 , l O l 3 )D O 5 1 0 1 = 1 , K O U N TW R t T f ( 6 , 1 0 0 0 ) I , ( X p a R ( I , J ) , J = 1 , 1 2 )
5 1 0 C O N T I N U E
98W R T T F ( 6 , 1 n i 4 )0 0 5 n 1 = 1 , KOUNTW R î T r ( 6 , l O O O ) T , ( S T r,M A ( î , J ) , J = 1 , 1 2 )
511 r O N T l N U FW R t T f ( 6 , 1 Ù 1 5 )0 0 5 1 ? 1 = 1 , KOUNTWR T T f ( 6 , 1 J 1 6 ) I , ( ( ROT ( J , I CHAN , JCH AN ) , JCHAiN= 1 , 1 2 ) , I f h a N = 1 , 1 2 )
'^1? CON T I N UE0 0 5 1 ^ T = 1 , N C L U S TI F ( M f Rc f ( T ) , r . T , K O U N T ) r -0 TO 6 1 4WRt T f ( 6 , 5 1 F ) T , M F R C F ( T )
5 1 5 FORf /AT ( I X , 7 h c L U S T f r , t 4 , i x , 5 h C L a S S , T 4 )5 1 1 C O N T I N UF 5 1 4 CONT I NUE
0 0 6 6 0 1 = 1 , KOUNT 0 0 6 ? 0 I C H A N = 1 , N C H A N 0 0 6 1 0 J C H A N = l , N C H A NR ( I C H A N , J C H A M ) = R O T ( I , J C H A N , I C H A N ) / S I G M A ( I , I C H A N )
6 1 0 C O N T I N UF 6 7 0 CONT I NUE
0 0 6 5 0 i r H A N = l , NCHAN 0 0 6 4 0 K C H A N = 1 , N CH A N 61 iv = o , 00 0 6 1 0 JCHAN = 1 , NCHANS U M = S U M + R 0 T ( I , I C H A N , J C H A N ) * R ( J C H A N , K C H A N )
6 1 0 r O N T l N l l EA ( I C H A N , K C H A N ) = S U V
6 4 0 C O N T I N U F 6 5 0 r O N T l N U E
W R I T E ( 6 , 6 0 0 ) I 6 0 0 F O R M A T ! I X , 1 1 H C L A S 5 E L L I P S E , 1 6 )
W R t T e ( 6 , 1 0 0 5 ) ( ( A ( T A , J a ) , J a = 1 , N c h a N ) , t a = 1 , N c h a N )6 6 0 CONT I NUE
RF' - ' INO LTPr e t u r nEND
9 9
St i pROUTî Nc- F F T r O R ( T f L a G , C »NPOP j N f L p , N )
rOMMON / L A p 1 / X P 4 R ( 4 3 » 1 2 ) , S T f M a ( 4 3 , 1 2 ) , R 0 T ( 4 3 , 1 2 , 1 2 )COMMON / L a q 2 / X ( 1 2 ) , a L P h A ( 4 9 ) , N 5 P S , N S C A N S , N c H a N , L T 9 , L T 1 0 »L T 1 1 , L T 12 »
1 L T 1 3 , L T 1 , I X , I Y ,1 M C T A R T , N . 9 T 0 P ,1 N f T L C j M O f i F , T T Y P f , V c ; p c , T 4 » N c R f ,
i N S K î P , î N r X , T N C Y , N 5 T X , N S T Y « n i ^ F N S I O N N P O P d ) , r ( 4 3 » 7 P ) » M 0 A T { ? 3 F ) d a t a N C N T / 0 /ÎNI,IM = 0N F L G 1 = 0
N F L G P = 0DO 5 I C H A N = 1 , N r H A N
X q A R ( T A r , , T r M A N ) = 0 , 0 * nO 1 0 J CHAN= T C MA N » N r H A N
I NI . . ' M=I NUM + 1 C ( T F L A G , T N U M ) = 0 . 0
10 C O N T I N U F 5 C O N T I N U F
<NT = 04 0 C O N T I N U F
I F ( N C N T . G F . N S f a N F ) GO TO 7 0 N F L G ? = 0R F A n ( L T l 2 ) ( N n A T ( J J ) , J J = 1 , N S P S )n c n t = n c n t + i
N F L G I =1N F L A G ? = 10 0 2 0 J J = T , N G P qCALL G F T ( X ( 1 ) , N S P S , 0 , N c H A N , N S C A N G , L T 1 0 , t f R R , M p L A G 2 ,
l N S T A R T , N P T L G , ^ O O F , N r R F , T T Y P F , M S F C )I F ( N O A T ( J J ) . N F . N ) PO TO POK N T = K N T + TN F L G 2 = 1A I = F L 0 A T ( K N T )
I N ' j M = 0DO I CHAN = 1 , NCHANX p a R ( I F L A G , T C H A N ) = ( 1 . 0 - 1 . 0 / A T ) * X P A R ( î F L A G , I C H A N ) + X ( T C H A N ) / A TnO 2 6 JCHA.N = I CHAN , N f h a NI NI I M= I N! J M+ 1r ( t '^L AG, J N U Y ) = ( 1 . 0 - I . 0 / A I ) * C ( T F L A C , t NUM ) + X I î ^ r a N ) * X ( J t m a N ) / A î
2 6 C O N T I N U F2 5 C O N T I N U F
GO TO 2 0 3 0 C O N T I N U E '
I F ( N F L G P . F Q . T ) r O TO 20TF ( M D A T ( J J ) . N F . M + I ) GOTO 20N5AV= NCNT N F L G P = i
2 0 C O N T I N U FC WR I t f { 6 , 1 0 0 0 ) NcNT , KNT , N S A V , NpcKi j P , N , N f L g 2 , N f L g p
1 0 0 0 F O R M A T ! I X , 7 1 3 )I F . ( N F L G 2 . N F . 0 ) GO TO 4 0I F ( N F L G P . F Q . 0 ) r-0 TO 4 nN p r K U P = N r N T - N 5 A V + l r a l l p G R f c d ( L T 1 0 , N p c K U P * I 4 , R F )
1 0 0
S U R C O U T I M F A M T R X ( I F L A ^ , X R A R , r , A , M r w A N l n y V r N s i O N X r a R ( 4 T , 1 ? ) , r ( 4 ^ » 7, n )
nOl. iRLF P R E C I S I O N A ( i ? , i ? )INMMrOno 1 î ^ H A N = i , MrHaM no ? j r H A M = T r w A M , M r w A M I M ' J V = î M U M + 1A ( I C H A M , J C H A M ) = C ( I F L A G , 1 MUM) - X B A R ( I F L A G , I C H A M ) * X B A R ( I F L A G . J C H A M ) A ( JCHAN , I CHAN ) = A ( I r(JAN , J t h a V.)
? CONTI NU' "1 CON T I N UF
RFT' iRN PNn
S ' R 0 U T I M F R 0 T A ( I F L A G , R0 T , P I G1“ M , N C H A N , A , 5 î G'-1A 1ni MFNSl ON R 0 T ( 4 G , 1 R , 1 ? )n T ^ ^ NS l OM G Tg Ma ( 4 ? , 17 )nOlJRLP P R E C I S I O N A ( i ? , l ? )n'Mjn.i r pprrjGTn,v r t r,cN ( i ? , i 7 )no 1 I C H A N = I ,NrwANS I G M A ( I f l a g , I C H A M ) = A ( I CHAM, I CH A N ) n o ? J C H A N = 1 , NCHANROT ( I F L A r - , I CH AN , JCH AN 1 =F I r, r,M ( j r n AN , I C H A N )
? C ON T I N UF1 OONTI MHP
RF TURN FNn
S U R R O U T l N r Sr u r r K ( T F L A G , ROT » X » S IGM A , AS' JM , NCM AN )n i V F N S T O N ROT ( 4 ? , 1 , 1 ? ! , S Î GM A ( 4G , I ? ) , X ( I )A c i i M = n , nn o 7 i r w A N c T , N r H A N
= 1n o 4 JCH A N = I , M'-H AMS!JV = 5UM + R 0 T ( I f l a g , t o h a M , J C H a n ) * X ( J o H A N )C O N T I N U FASM M = A S U M + S 1J Ai * S U M / S T G M A ( I F L A G , I C ! J A M )r O M T I N U Fp r y u R Nc-Ajn
101S U n R O U T î N F f L A S S { N r L A S S » N T f S T j N P a SS 1 rOMMON / L A R 1 / X R A R ( 4 3 » 1 2 ) ♦ S T r,M a ( 43 , 1 2 ) , ROT ( 4 3 , 1 2 , 1 2 ) rOMMON / L A R 2 / X ( 1 2 ) , a L P h A ( 4 9 ) , N S P S , N S r A N S , N r H A N , L T 9 , L T l 0 , L T l 1 , L T 1 2 ,
1 L T 1 3 , L T 1 , I X . , N D U M M Y ,1 N S T A R T , N S T O P ,l N R T L 0 , M 0 n F , l T Y P P , M q F r , I 4 , N r R f ,1 N . S K I P , i N c X , I N C Y , N 5 T X , N S T Y
n î M R N S î O N W ( 1 2 ) , ^ T A P ( R )O I M R N S I O N N n A T ( 2 5 3 , P ) , P R N T ( 2 5 5 )HTWENSI ON C Q M ( 2 4 )F Q U î V A L P N r R ( C O M ( 1 ) , N S P S )REWI ND L T 9 RPWI ND L T l O RPWI ND L T l RPWI ND L T l 2 Re w i n d l t i 3r Z P r H = N r H A NI F ( N S K I P . P O . 0 ) GO TO 60%DO 6 0 2 I = l , N S K î P C AL L S K R R I N ( L T l O , l , N O P )
6 0 2 C O N T I N U ^601 CON T I N UF
Rp a d ( L T 9 ) ( p OM( I ) , t = 1 , 2 4 )Rp a D ( L T 9 ) ( ( X h a R ( r , J ) , I = l , N r L A S 5 ) , J = 1 , I 2 )RPAD ( L T 9 ) ' ( ( 6 i r -M A ( T , J ) , I =1 , N r L a SS ) , J = 1 , 1 2 )R P A D ( L T 9 ) ( ( ( R 0 T ( I , i r H A N , J r w A N ) , I = l , N r L A 5 5 ) , i r H A N = l , N r w A N ) ,
1 J r M AN = l , M r H A N )DO 1 1 = 1 , 3
1 ' n A R ( i ) = iDO 10 I F N D = 1 , N 5 C A N SRp a d ( L T 1 2 ) ( N d a T ( I ,1 ) , 1 = 1 , NSPS)N P L A G ? = iDO 20 I S U p N = i , NSPSr A L L G P T ( X ( 1 ) , N S P S , 0 , N r H A N , N S P A N O , L T I O , I p R R , N F L a G 2 ,
1 M 5 T A R T » N P T L G , M C n p , N P R F , T T Y P P , M S P C : )I P (NDAT ( l S ' . J o M , l ) . G T , 0 ) NRAT ( I SUpN , 1 ) =:-'!
SV A L L = 1 . 7 3 * C 7 - F p h DO 23 I G L A S S = 1 , N C L a f S nO 3 0 I p h a N = 1 , N r n A NW ( I C H A N ) = X ( I C H A N ) - X H A R ( I CLASS , I C H A N )
30 p QNTTNUF A.ci . tMsO.ODO 3 5 I C H A N = 1 , NCHAN Cl i Ms O. 0n o 4 0 JCHAN = l, , NCHANSUM=SUM+W( J c h A N ) * R 0 T ( Tp L a S S , I C H A N , J c H A N )
40 C O N T I N U F4 1 a S U M = a S U M + S U M * 5 U M / S T G M a ( i c L a S S , I C H a N)
35 CON T I N UPI F (ASUM . G T . S M A L L ) GO TO 2 5 s m a l l = a s u m
N d A T ( I S U R N , ! ) = I CLA,SS 25 CON T I N UF 1 0 1 6 p ORMa T ( 1 X , 3 1 6 » F 1 0 . 2 )2 0 C O N T I N U P
1 0 2
W R t T c ( L T I ) ( N n A T ( T , 1 ) » î = l »NSPS)10 r O N T l N U F
e n d F I L E L T IRe w i n d l t iREWI ND L T l ?REWI ND L T I O DO 6 1 0 I Z = 1 , N S C A N S I V = M T A R ( 1 )R p a d ( L T 1 ) ( N d a T { T A , t Y i , T A = 1 » N 5 P S ) N T c w P = Y T A n ( 1 )
M T A F ( 1 ) = X T A R ( ? )M T A P ( ? ) =MT A R ( R )v1 T A R { ^ ) = N T E M PTF ( TZ . L T . R ) GO TO 6 1 0n o 6 p O I A = N S T A R T . , N c t OPTF ( T A . P Q . 1 ) GO TO 6 ? 0TP ( J A + 1 . P - T . N S T O P l PC TO 6?DT I Y=v i TAn ( ? )TP ( NPASS . P Q . N T F S T ) GO TO 621 TP ( N D A T ( T A , T T Y ) . L T . 0 ) GO TO 6 2 0
621 C O N T I N U EIM=MTAR(1)I N = M T A R ( ? )M = N D A T ( T A » T M )N = M DA T ( T A - 1 , T N )TF . N P . N) GO Tn 6 p 0 I L = M T A R ( R )L = N D A T ( I A » I L )I F (Y . N F . L ) GO TO 6 5 0 N D A T ( I A , I I Y ) = M GO TO 6 2 0
6 p 0 T M = M T A P (1 )m = Npi aT ( T A - 1 , t Y)T N = M T A R ( R )N = NDA.T( I A - 1 , I N )I F ( ' " . N F . N) GO TO 6 ? 0 L = N D A T ( l A + l , I M )TR (M . N F . L ) GO TO 6 2 0 N n A T ( . I A , T I Y ) = M
6 ? 0 C O N T I N UEI P ( I Z . L T . R) r- 0 TO 6 1 0 L=WTAP( 1)WR T T p ( L T l 3 ) ( Nr a T ( T , L ) , I = 1 » N S P S )
6 1 0 C O N T I N U PDO 611 1 = 2 , R L = W T A R ( I )WRTTp C L T i R ) ( N r a T ( T L , L ) , I L = 1 , N S P S )
611 O O N T t NUF RP' - ' IND L T l REWI ND LTD RPWI ND L T i R REWI ND L T l 0l o w = n s t a r t
LWFR=1 POO C O N T I N U E
103Nh t = L O W + i 7 0 - 1 N U P P F R = L W P R + 1 ? 0 - iI P ( NUPPPR . G T . NSPS ) NUPPPR= NSPST n i F = N U P P F R - L W F R + lW R T T E ( 6 » 1 0 0 7 )
1 0 0 7 F O R M A i d H I )c a l l L A R F L A ( L O W , N H T , 1 )no SOI t t = i , n s c a n sR P A n ( L T T 7 ) ( N n A . T ( J J , 1 ) , J J = l , N S P S ) n o 8 0 3 J J = L W F R , M U P P p R T P s N n A T ( J J , 1 )T R N n = T R - ( i n - l ) / 4 F * 4 S + 2 P R M K J J ) = A L P H A ( l R N n )
8 0S C O N T I N UEf a l l P L T p f a ( P R N K L w p R ) , I n i F , N r L K , I N c X , I N c Y , N 3 T X , N S T Y , N r R F ,
1 i NPL ACX , N f L A G I )WR Tire ( 6 , 1 0 0 8 ) t T , ( P R N T ( J J ) , J J = L W P R , N U P P c R )
1 0 0 8 F O R M A T ( 4 X , I 6 , i H * , 1 ?0A 1)8 0 1 C O N T I N U E
R P Wl Nn L T l 3 N FLAG1=0 NFLAGX = r'L WPR= NUPPFR+iL O w = N H l + ii r ( N U P P F R . L T . N S P S ) G O T O 8 0 0
8 0 3 r O M T I N U FNSCANS = N s r A , N S - 7R p TURNFNn
APPENDIX C
Channels Dependence C o n sid e ra tio n s
Iso m e tr ic p lo t s and p r o b a b i l i ty d i s t r i b u t io n s o f each channel o f
d a ta , a long w ith th e j o i n t p r o b a b i l i ty d i s t r i b u t io n s betw een p a i r s o f
c h a n n e ls ,w e r e examined to e s ta b l i s h a g e n e ra l view o f th e Purdue
F l ig h t L ine Cl d a ta . T his g e n e ra l view was th en used in develop ing
th e c l a s s i f i c a t i o n scheme p re se n te d in th e t e x t , b u t one a re a o f
a n a ly s is was n o t d is c u s s e d . T his a re a i s concerned w ith channel
dependence and w hether i t i s n e c e ssa ry to use a l l channels o f d a ta
o r on ly a few s e le c te d ch anne ls to o b ta in a re a so n a b le degree of
c l a s s i f i c a t i o n su c c e ss . The purpose o f t h i s s e c t io n i s to d isc u ss
th e p ro s and cons o f u s in g a l l ch anne ls o f d a ta v e rsu s a few s e le c t
ch an n e ls o f d a ta .
In d ic a t io n s o f Channel Dependence
E xam ination o f th e is o m e tr ic s p lo t s o f th e d a ta re v e a le d th a t
i t was v e ry easy to v i s u a l ly c o r r e l a t e a l l p o r t io n s o f th e d a ta to
th e pho tog raph o f th e ground sc e n e , and th i s was t r u e fo r a l l channels
o f th e d a ta . Many o f th e ch an n e ls o f th e d a ta appeared p h y s ic a l ly
s im i la r , a lth o u g h th e d a ta becomes p h y s ic a l ly n o is ie r in th e in f r a r e d
c h a n n e ls .
104
105
Exam ination o f th e j o i n t p r o b a b i l i ty d i s t r ib u t io n s a ls o in d ic a te d
th a t th e re m ight be a l i n e a r dependence betw een s e v e ra l ch an n e ls . The
j o i n t p r o b a b i l i ty d i s t r i b u t io n s betw een th e f i r s t 6 channels appeared
sim ilar" and p o s s ib ly l i n e a r . The same was t r u e w ith channels 7
th ro u g h 10 and channe ls 11 and 12. However, d e g rad a tio n in th e
s im i l a r i t y was n o tic e a b le in th e j o i n t p r o b a b i l i ty d i s t r ib u t io n s
betw een channe ls th a t became f a r th e r a p a r t s p e c t r a l ly . For exam ple,
th e j o i n t p r o b a b i l i ty d i s t r i b u t i o n betw een channels 1 and 2 appeared
v e ry s im ila r to th e j o i n t d i s t r i b u t i o n betw een ch anne ls 5 and 6, b u t
th e j o i n t d i s t r i b u t i o n betw een channe ls 1 and o appeared s l i g h t ly
d i f f e r e n t .
These o b se rv a tio n s r e v e a l th a t i t may be p o s s ib le to p re d ic t
o th e r channel m eans, v a r ia n c e s , and co v a rian ces used in th e e l l i p t i c a l
d e c is io n r u le from th e means, v a r ia n c e s , and co v arian ces o f a s e le c te d
channe l o f d a ta . I f t h i s i s p o s s ib le , th e n th e c a lc u la t io n s o f th e
m eans, v a r ia n c e s , and c o v a rian ces from th e raw d a ta could be e lim in a te d .
I f th e l i n e a r p r e d ic t io n c o n ta in e d v e ry l i t t l e e r r o r , th en i t would
a ls o be p o s s ib le to e l im in a te th e p re d ic te d channel o f d a ta e n t i r e ly ,
s in c e i t would c o n ta in v e ry l i t t l e new in fo rm a tio n .
F ig u re 29 i s an in d ic a t io n o f th e j o i n t p r o b a b i l i ty d i s t r i b u t io n
betw een ch anne ls 1 and 2 . The l in e d a re a s c o n ta in no d a ta p o in t s ,
w h ile re g io n 1 c o n ta in s a t l e a s t one occu rren ce o f each d a ta p o in t
and may c o n ta in as many as 37 o ccu rren ces o f each d a ta p o in t . Region 2
c o n ta in s th e crop sym bols, as i d e n t i f i e d on page 32, and has as few
as 38 o ccu rren ces o f each d a ta p o in t to as many as 1,702 occurrences
106
vu w
'Ta ©
RBGION 1
« 182REGION 2
= 180 <u
ss su
REGION 1
160 162 164 166 168 170 172 174 176 178 180 182 184
Channel 1 Mean Values
FIGURE 29
CHANNELS 1 AND 2 MEAN V A LUES
107
o f each d a ta p o in t . The crop symbols r e p re s e n t th e lo c a tio n s o f
th e mean v a lu es o f th e f i r s t 75 i n i t i a l c lu s t e r s o f th e Purdue d a ta .
Region 2 appears to be a l i n e a r re g io n and th e lo c a t io n o f th e mean
v a lu es o f th e c lu s t e r s appear to be l i n e a r ly d i s t r i b u te d , a lth o u g h
s e v e ra l c rop types would have d i f f e r e n t in te r c e p ts fo r t h e i r r e g re s s io n
l i n e s . F ig u re 29 a ls o in d ic a te s why i t i s d i f f i c u l t to c l a s s i f y
c o rn and soy as being d i f f e r e n t f e a tu r e s . The p ro b ab le re a so n fo r t h i s
d i f f i c u l t y i s th a t b o th crops a re row crops and th e scanner f i e l d o f
view is averag ing over an a re a c o n ta in in g a c e r t a in p e rce n tag e o f
b a re s o i l and v e g e ta t io n . The c o n d itio n and type o f s o i l cou ld a ls o
v ary w ith in th e ground scene f u r th e r co m p lica tin g th e s e p a ra t io n o f
bo th f e a tu r e s . The non row crops such as o a t s , w heat, and ry e appear
re a so n a b ly d is t in g u is h a b le . F ig u re 29 a ls o i l l u s t r a t e s how in fo rm a tio n
could be l o s t i f channel 2 w ere re g re s se d on channel 1. The o a t ,
w heat, and rye in fo rm a tio n would be com pressed in to a l in e c o n ta in in g
th e soy and co rn in fo rm a tio n , and th e re fo re cou ld p o s s ib ly be l o s t
u n le ss th e in fo rm atio n cou ld be d is t in g u is h e d in an o th e r s e t o f ch an n e ls .
F ig u re 30 in d ic a te s in fo rm a tio n s im ila r to f ig u re 29, excep t
th a t th e in fo rm a tio n in channel 3 i s p lo t te d v e rsu s channel 1. A gain,
re g io n 2 appears l i n e a r . The mean v a lu es from th e non row crop c lu s t e r s
a ls o appear l i n e a r , b u t t h e i r s lo p es and in te r c e p ts have changed
s l i g h t l y . A re g re s s io n between th e se two channe ls would in d ic a te a
more se v e re lo s s o f in fo rm a tio n th a n in f ig u re 29, because o f the
s lo p e changes.
204
REGION i
REGION 2
/ /^REG IO N 1
1----------- r1 6 0 1 6 2 1 6 4 166 168 1 7 0 1 7 2 174
C h a n n e l 1 Me a n V a l u e s
FIGURE 30
C H A N N E L S 1 A N D 3 MEAN V A L U E S
176 178 1 8 0 182 1 8 4
o00
109
F ig u re s 31 , 32 , 33 , and 34 i l l u s t r a t e th e d i s t r i b u t io n and
v a r ia n c e s and c o v a ria n c e s o f th e crop c lu s t e r s co n ta in ed in channe ls
1 and 2 and ch an n e ls 1 and 3 r e s p e c t iv e ly . The v a r ia n c e s and c o v a rian ces
do n o t ap p ea r to be se p a ra b le acc o rd in g to crop ty p e , b u t do appear
to be l i n e a r ly d i s t r i b u t e d . The g raphs o f th e c o v a rian ces v e rsu s th e
v a r ia n c e s appear to c o n ta in le s s s c a t t e r th a n th e graphs c o n ta in in g
o n ly v a r ia n c e s , becau se o f th e common channel used in bo th c a lc u la t io n s .
P ros and Cons
Two g e n e ra l s ta te m e n ts can be made concern ing th e use o f a l l
ch an n e ls v e rsu s a s e le c te d few ch an n e ls o f d a ta . F i r s t , i f a few
ch an n e ls o f d a ta cou ld be s e le c te d th a t would g iv e re a so n a b le su ccess
i n c l a s s i f y in g th e ground scen e , th e n th e re would be a requ irem en t
fo r n o t re c o rd in g th e u n s e le c te d ch an n e ls o f d a ta , le s s d a ta to manage,
and le s s tim e re q u ire d fo r th e m a th em atica l com pu ta tions. On th e
o th e r hand , u s in g a l l ch an n e ls o f d a ta im p lie s ta k in g advan tage o f
n s im u ltaneous m easurem ents and hence th e maximum d is c r im in a t io n
a b i l i t y o f th e d a ta .
The second s ta te m e n t th a t can be made i s th a t th e c l a s s i f i c a t i o n
scheme used w i l l p a r t i a l l y de te rm in e w hether a s e l e c t few or a l l
ch an n e ls o f d a ta w i l l be u t i l i z e d . For exam ple, th e su p e rv ised
m ethods a re u s u a l ly more a d a p tiv e to s e le c t in g a few channe ls o f d a ta .
The su p e rv ise d approached has th e b e n e f i t o f a p r i o r i knowledge o f th e
ground scene w hich can be u t i l i z e d . I f th e lo c a t io n s o f s e v e ra l
f e a tu r e s a re known in th e ground sc e n e , th e n th e d a ta can be examined
to de te rm in e how many ch an n e ls a re needed to c o r r e c t ly c l a s s i f y each
110
1 2 -
10 -
tn<uoc
o>
s cOJ
oo
cw
ws
10 122 864
Ch a n n e l 1 V a r i a n c e s
FIGURE 31
C H A N N ELS 1 A N D 2 V A R IA N C E S
6 -
c/>o>o
o>
a>cco_co e c u
8 10
N
12C h a n n e l 1 V a r i a n c e s
FIGURE 33
C H A N N E L S 1 AND 3 V A R IA N C E S
t/>0>oco>oo
0>cco
r u W co
0S
0 8 10
OJ
12C h a n n e l 1 V a r i a n c e s
FIGURE 34
C H A N N E L 1 V A R IA N C E S AND C O V A R IA N C E S WITH C H A N N E L 3
114
f e a tu r e and n o t m i s d a s s i f y th e o th e r known f e a tu r e s . One f e a tu r e may
r e q u ir e 3 ch an n e ls fo r c o r r e c t c l a s s i f i c a t i o n , w h ile an o th e r f e a tu r e
f e a tu r e may r e q u ir e 3 d i f f e r e n t ch a n n e ls , and an o th e r f e a tu r e may
on ly r e q u i r e 2 ch a n n e ls . Using t h i s type p f in fo rm a tio n cou ld le ad tc
e l im in a t io n o f some channe ls o f d a ta . A re d u c t io n in th e number o f
ch an n e ls w ith o u t re g a rd to th e f e a tu r e s c o n ta in ed in th e d a ta u s u a lly
enhances th e c l a s s i f i c a t i o n o f some f e a tu r e s , b u t a t th e same tim e
in c re a s e s th e d i f f i c u l t y o f s e p a ra t in g o th e r f e a tu r e s . I f a d i f f e r e n t
s e t o f ch an n e ls i s used f o r each f e a tu r e , th e n re a so n a b le s e p a ra t io n
o f a l l f e a tu r e s can u s u a l ly be ach iev ed . However, th e re i s no
g u a ra n te e th a t an unknown f e a tu r e w i l l be c a l s s i f i e d c o r r e c t ly .
The u n su p e rv ised approach p re se n te d in th e t e x t was developed fo r
th e a n a ly s is o f th e E a rth R esources Technology S a t e l l i t e d a ta , which
i s a c o n s id e ra b le volume o f d a ta . For exam ple, each image from th e
s a t e l l i t e co v ers ap p ro x im ate ly 10,000 square m ile s , and , because o f
th e c o s t and e f f o r t , a p r i o r i knowledge or ground t r u t h c o l le c t io n
needs to be m inim ized and o p tim ized . This can be accom plished only
a f t e r th e d a ta has been an a ly zed , s in c e th e r e s u l t s o f th e a n a ly s is
a re d esig n ed to in d ic a te w here ground t r u t h c o l le c t io n i s needed. For
t h i s re a so n i t may be more r e l i a b l e to u se a l l ch an n e ls o f d a ta fo r a
maximum amount o f d is c r im in a t io n a t th e c o s t o f more com puter tim e.
The f i n a l d e c is io n conce rn ing w hether o r n o t to u se a l l channels
o f d a ta appears to be co m p lica ted by many in p u ts and tr a d e o f f s fo r
th e u n su p e rv ise d te ch n iq u e p re se n te d in th e t e x t . Computer ro u tin e s
and c r i t e r i a co u ld be developed f o r d ec id in g w hich channe ls a re to be
115
co n s id e re d l i n e a r ly dependen t. The c r i t e r i a f o r l i n e a r dependence
would then have to be e v a lu a te d by c o n s id e r in g th e amount o f in form a
t i o n lo s t in th e c l a s s i f i c a t i o n when th e t o t a l number o f channe ls
i s reduced . The second c o n s id e ra t io n concerns th e amount o f com puter
tim e re q u ire d fo r d e te rm in in g channel dependence and c l a s s i f i c a t i o n
v e rsu s c l a s s i f i c a t i o n u s in g a l l channe ls o f d a ta . A d d itio n a l in p u ts
to th e se c o n s id e ra tio n s a re th e t o t a l number o f channe ls o f d a ta th a t
a re reco rd ed and th e s p e c t r a l bandw idth lo c a t io n s . I f many channe ls o f
d a ta a re re c o rd e d , i t may be w orthw hile to reduce th e number o f channe ls
used in th e c l a s s i f i c a t i o n from l in e a r dependence c o n s id e ra tio n s . On
th e o th e r hand , i f on ly a few channe ls a re re c o rd e d , i t may be f a s t e r
to c l a s s i f y th e d a ta u s in g a l l o f th e channe ls w ith o u t l in e a r dependence
c o n s id e ra tio n s . T h ird ly , and assumming th a t th e same sen so r is being
u sed , th e re i s th e q u e s tio n o f w hether o r n o t th e channel dependence
c o n s id e ra tio n s w i l l rem ain in v a r ia n t fo r d a ta c o l le c te d a t d i f f e r e n t
t e s t s i t e s , which c o n ta in c o n s id e ra b ly d i f f e r e n t ty p es o f t e r r a i n
f e a t u r e s .
The m ain re a so n fo r n o t in c lu d in g channe l dependence in th e d e v e l
opment o f th e u n su p erv ised approach is th a t th e e v a lu a tio n o f th e
c o n s id e ra tio n s p re se n te d above can on ly be o b ta in ed a f t e r th e d a ta has
been analyzed and ground t r u t h in fo rm a tio n has been c o l le c te d . The
in fo rm a tio n i s needed p r io r to th e d a ta a n a ly s i s , i f i t i s to be
u t i l i z e d e f f i c i e n t l y .